IN  MEMORIAM 
Johlr'Swett 


FRENCH'S  MATHEMATICAL  SEHffi$v  •  \V  , 


MENTAL  ARITHMETIC; 


COMBINING  A 


COMPLETE  SYSTEM  OF  RAPID  COMPUTATIONS, 


CORRECT  LOGIC  OF  THE  SOLUTIONS  OF  PROBLEMS, 
AND  THE  ANALYSES  OF  PROCESSES. 


BY 

JOHN  H.  FRENCH,  LL.D. 


Mental  Arithmetic   is  tht  Logic  of  the   Common   School. 


NEW  YORK : 
HARPER  &  BROTHERS,  PUBLISHERS, 

FRANKLIN    SQUARE. 
1872. 


1C          -N  DEP  • 

PUBLISHERS'  NOTICE 


FRENCH'S  ARITHMETICS. 

This  Series  consists  of  Five  Books,  vis. : 

I.    FIRST    LESSONS    IN    NUMBERS. 
II.    ELEMENTARY    ARITHMETIC. 

III.  MENTAL   ARITHMETIC. 

IV.  COMMON    SCHOOL   ARITHMETIC. 

V.  ACADEMIC    ARITHMETIC.      (In  prep* 


Tho  Publishers  present  this  Scries  of  Text-Books  to  American 
Teachers,  fully  believing  that  they  contain  many  new  ar 
able  features  that  will  especially  commend  them  to  t! 
wants  of  the  age. 

Tin-  plan  i'  -r  the  Scries,  and  for  each  book  embraced  in  it,  was 
fully  matured  before  any  one  of  the  Series  was  completed  ;  and  as 
it  is  baaed  upon  true  philosophical  principles,  there  is  a  hannmiv. 
a  fitness,  and  a  real  progreoriveneM  in  the  books  that  an  n<>t 
found  iu  any  other  Scries  of  Arithmetics  published. 


Entered  according  to  Act  of  Congrea*,  In  the  year  1870,  bj 

HARPER    &   BROTHERS, 
In  the  Office  of  the  Librarian  of  Congress  at  Washington. 


PREFACE. 


T3REVIOUS  to  the  introduction  of  tbc  study  of  Mental 
Arithmetic  into  American  schools,  pupils  were  seldom 
required  to  give  reasons  for  processes  of  computation ;  and 
few  teachers  could  be  found,  who  could  give  any  reason  for 
an  arithmetical  process  other  than  u  The  rule  says  so."  The 
publication  of  Warren  Colburn's  First  Lessons,  in  1826, 
marked  the  beginning  of  an  era  of  progress  in  the  art  of 
teaching.  The  use  of  that  book  turned  the  attention  of 
teachers  to  two  facts,  viz:  1st.  That  for  every  arithmetical 
process  there  is  a  reason  ;  and  2d.  That  it  is  quite  as  im- 
portant that  pupils  learn  the  why  as  the  how. 

The  general  principle  that  reformers  go  to  extremes,  found 
no  exception  in  the  case  of  the  introduction  of  the  study 
of  Mental  Arithmetic  into  our  schools.  The  chief  aim  of 
some  teachers  of  this  subject  seems  to  have  been,  to  see  how 
much  a  child  could  be  made  to  say,  in  solving  a  problem, 
rather. than  to  cultivate  his  power  to  combine  numbers,  and 
his  ability  to  explain  processes  and  state  reasons  clearly,  con- 
cisely, and  understandingly.  By  this  class  of  teachers,  much 
talking  has  been  regarded  as  indispensable  to  good  scholar- 
ship in  this  subject.  But,  within  the  past  ten  years,  many 
prominent  educators  in  different  sections  of  the  country  have 
had  sufficient  independence  to  question  the  value  of  the  dis- 
cipline resulting  from  lengthy  solutions,  recited  from  memo- 

541815 


.IV  PREFACE. 

>'•;(  ippmnja» -and  to  test  the  comparative  value  of  tlirsc  with 
'   concise  processes,  which  appeal  constantly  to  the  reason 
understanding  of  the  learners.     It  is  scarcely  needless  t 
mark  that.  win  n  v.r  these  testa  have  been  made,  they  have 
.ted  in  favor  of  concise  methods  of  solution. 

The  objects  for  which  children   should  study  Mental  Arith- 
metic are  two,  namely  :  First.  To  acquire  accuracy  ;. 
ity  in  combinations;   and  Second.  To   acquire  the 

.<on  correctly.    The  attainment  of  this  BCCOT.  will 

give  them  the  ability  to  combine  a  process  \\iih  a  reason,  and 
\ra\  statements  adapted  to  the  solution  of  prob- 
lems, which  shall  IT  i  rrcct.     In  th«-  i 
aration  of  thi-  work   these    I                   :s    have  )>een   kept 
stantly  in  view.      The  attention  of  teachers  and  parents  is 
especially  invited  to  the  following  general  plan  and  di>tin 
features  of  the  work  : 

<.«  m  r;il    Plan. — The  book  is  divided  into  * 
ten,  the  first  one  of  which  is  devoted  to  combinations  in 
integers  'in  which  no  result  exceeds  100,  and  is  called  a  1 

irse  in  Integers;  the  second  chapter  is  a  Second  Course  in 
Integers,  and  embraces  combinations  in  which  the  roults  do 
not  exceed  1,000;  the  third  chapter  is  devoted  to  United 
States  Money  ;  the  fourth  to  Compound  Numbers ;  the  fifth  to 
Fractions;  the  sixth  to  Converse  Operations  in  the  funda- 
mental rules,  and  in  the  reductions  of  Compound  Numbers 
and  Fractions;  the  seventh  to  the  five  general  case 
centage,  and  their  special  applications  to  Insurance-  Commis- 
sion, Profit  and  Loss,  Stocks,  Taxes,  Interest,  and  Discount ; 
and  the  eighth  to  Miscellaneous  Review  Problems, 

The  First  Course  in  Integers  is  designed  especially  for  chil- 
dren who  have  had  no  previous  instruction   in   Mental  Arith- 
metic.    Beginning  at  the  Second  Course  in  Integers, 
the  order  of  subjects  is  the  same  as  that  in  the  Common  School 


PREFACE.  V 

Arithmetic  ;  and,  from  this  place  to  the  end  of  the  book,  the 
two  works  can  be  used  together,  the  same  subject  in  the  two 
books  being  studied  at  the  same  time.  This  arrangement  has 
received  the  approval  of  many  of  the  best  teachers  in  the  land. 

I>rill§  on  Combinations.— The  Addition,  Subtrac- 
tion, Multiplication,  and  Division  tables  are  omitted.  Thor- 
ough drills  in  the  exercises  given  on  pages  15,  17  to  22,  27, 
30  to  35,  41,  51,  and  52  will  make  pupils  accurate  and  rapid 
in  every  possible  combination  of  numbers. 

Problems. — These  are  all  new,  and  being  prepared  from 
material  gathered  from  the  various  departments  of  actual 
business  life,  are,  in  numerous  instances,  the  medium  of  in- 
struction in  the  usages  of  business,  and  the  uses  of  business 
terms  and  expressions. 

Illustrations. — The  cuts  and  diagrams,  all  of  which  were 
designed  and  engraved  especially  for  this  work,  possess  the 
superior  artistic  merit  which  has  been  conceded  to  the  illus- 
trations in  the  other  works  of  this  Series. 

Manual. — A  manual  occupies  the  last  ten  pages  of  the 
work.  The  first  three  pages  of  this  Manual  contain  hints  and 
suggestions  to  teachers,  references  to  which  are  made  in  the 
body  of  the  work  ;  and  the  last  seven  pages  present  methods 
of  solving  the  different  classes  of  problems  found  in  the  book, 
and  arc  embraced  together  under  the  head 

Methods.— All  methods  for  the  solution  of  problems 
being  omitted  from  the  body  of  the  work,  are  here  placed 
together,  and  are  referred  to  after  the  problems  to  which 
they  apply.  These  Methods  are  intended  as  models,  to  be 
varied  at  the  discretion  of  the  teacher.  They  are  logical  and 
progressive,  while  they  avoid  all  useless  verbiage  and  repe- 
tition. 

The  arrangement  of  the  subjects,  the  manner  in  which  they 
are  presented,  and  the  methods  for  the  solution  of  problems, 


vi  P  B  J 

have  constant  reference  to  the  healthful  development  of  the 
mental  powers  of  the  learner,  conducting  him,  in  an   i 
ruj)tcd   progress,  from  the  easy  to  the  difficult ;  pr 
him  but  one  new  difficulty  at  once,  and  giving  him  • 
pra.-tiei-  to  enable    him  to    ma.-U-r   that    difficulty  li  l\>:-< 
ing  it. 

:idently    belii-vcd    that    tin-    nbundaiit    ]>ra(  : 
combinations,  in  connection  with   the  solution  of  the  great 
number  of  easy  problems  given   in   the   First  Course   in   In- 
tegers, can  not  fail  to  make  children  in  combinations 
of  numlxTs:    while  the  very  large  number  of  well    graded 

DM  in  the  wor'.,.  mgp  in  the  pr 

afTiirs  Ofltts  will  atlord   th-   pmeti  .-ipline  tl 

them  to  compute  rapidly,  and  reason  logically  axd 
-cly. 


$ 
'  ^ 


CHAPTER   I. 


FIRST  COURSE  IN  INTEGERS. 


SECTION    I. 

DEFINITIONS 


A  Unit  is  a  single  thing,  or  one,  of  any  kind  :  as,  one  apple, 
one  bushel,  one  dozen. 

A  Number  is  a  unit,  or  a  collection  of  units. 

A  Concrete  Number  is  a  number  applied  to  some  object  ; 
as,  four  men,  ten  gallons,  fifty  quires. 

An  Abstract  Number  is  a  number  not  applied  to  any 
object  ;  as,  four,  ten,  fifty. 

An  Integer  is  a  number  the  units  of  which  are  whole  or 
undivided.  Integers  are  also  called  Whole  Numbers. 

The  use  of  numbers  in  estimating  quantities  and  values  in 
the  practical  affairs  of  life,  is  the  Art  of  Computation  ; 
and  a  proper  classification  and  arrangement  of  the  definitions, 
principles,  and  rules  used  in  computations,  is  the  Science  of 
Numbers.  Hence, 

Arithmetic  is  the  science  of  numbers,  and  the  art  of  com- 
putation. 

In  writing  numbers  for  computations,  ten  characters,  called 
Figures,  are  used. 

The  figure  0,  called  cipher  or  naught,  denotes  nothing,  or  the 
absence  of  number.  The  other  figures  represent  the  first  nine 
integers,  and  are  sometimes  called  digits. 


8 


FIRST     COURSE     IX     INTEGERS. 


The  t  nrc^- 

3,       4,       5,       6,       7,       8,      9, 
\    naught,  one,    two,  three,  four,  Jive,     tix,   wren,  eight,  nine. 

To  express  numbers  greater  than  9,  two  or  more  of  the  ten 
figures  must  be  combined. 
.livery  ten  one*  taken  together  are  called  a  ten. 

Ten  is    written     10 

•i-.  or  twenty,  are  written     90 

8  tens,  or  thirty,  "  SO 

4  tens,  or  forty,  40 

5  tens,  or  fifty, 

C  tens,  or  sixty,  CO 

ns,  or  seventy,  70 

8  tens,  or  eighty,  SO 

9  tens,  or  inn  *4     90 

Whon  two  figures  an  ™  ritt  n  together  to  express  a  number, 
the  Irft-h.ind  figure  expresses  ten*,  and  th  ri-ht-hand  figure 
one*.  Thus, 

Fourteen        consists  of  1  ten   and  4  ones,  written  14 

ity-threc 
Thin 

" 

Fifty -nine 
Sixty-seven 
Seventy-eight       " 
Eighty-one  " 

Ninety 

1.  "\Vrite  in  words  the  following  numbers: 
89,  91, 17,  40. 

2.  Write  in  words  61.  08. 

3.  How  many  are  expressed  by  each  of  the  foil. 
numbers :  63,  72,  9,  56,  43,  25,  10. 

£  Write  in  words  73,  55,  18,  85,  32,  90,  27,  20. 
5.  Express  by  figures  the  following  numbers:  thirty, 
eleven,  twenty-six,  lifty-1. 


2  tens 

.. 

3  ones. 

t 

fft 

:j  tens 

6  ones, 

. 

1       S6 

4  tens 

H 

5  ones. 

. 

'      45 

5  tens 

u 

9  ones, 

i 

59 

0  tens 

H 

7  ones. 

i 

7  tens 

H 

S  ones. 

78 

8  tens 

a 

1  one, 

i 

81 

U 

0  ones, 

90 

DEFINITIONS    AND    NOTATION.  9 

6.  Express  by  figures  eighty-seven,  thirty-four,  nine- 
teen, seventy-two. 

7.  Express  by  figures  forty-one,  eight,  sixty-four,  ninety- 
nine. 

Every  10  tens  taken  together  are  called  a  hundred. 

10  tens  are  one  hundred,  -written  100 

20  tens  are  two  hundred,  "  200 

30  tens  are  three  hundred,  "  300 

40  tens  are  four  hundred,  *•  400 

50  tens  are  five  hundred,  "  500 

60  tens  are  six  hundred,  "  600 

70  tens  are  seven  hundred,  u  700 

80  tens  are  eight  hundred,  "  800 

90  tens  are  nine  hundred,  "  900 

When  three  figures  are  written  together  to  express  a  number, 

the  left-hand  figure  expresses  hundreds,  the  middle  figure  tens, 

and  the  right-hand  figure  ones.     Thus, 

172  is  one  hundred  seventy-two,  or  1  hundred  7  tens  and  2  ones. 

863  "  eight  hundred  sixty-three,  "  8  hundreds  6  tens   "    3  ones. 

351  "  three  hundred  fifty-one,      "  3 hundreds 5 tens   "    lone. 

408  "  four  hundred  eight,  "  4  hundreds  0  tens   "    8  ones. 

619  "  five  hundred  nineteen,        "  5  hundreds  1  ten     •*    9  ones. 

8.  Write  in  words  the  following  numbers:  100,  700, 

520,  9GO,  340,  210,  470.      (Sec  Manual,  page  171.) 

9.  Write  in  words  444,  591,  716,  343,  434,  2G8. 

10.  How  many  arc  expressed  by  each  of  the  following 
numbers :  254,  309,  207,  702,  506,  104,  999  ? 

11.  Express  by  figures  the   following  numbers :    two 
hundred,  seven  hundred  sixty,  three  hundred  seven- 
teen, four  hundred  fifty-nine. 

1,1.  Express  by  figures  three  hundred  seventy-four,  one 
hundred  eight,  five  hundred  two,  three  hundred 
seven,  seven  hundred  three,  three  hundred  seventy, 
seven  hundred  thirty,  nine  hundred  ninety-nine. 


10  FIRST    CO  U  BSE    IX     INTEGERS. 

In  writing  numbers,  every  10  hundreds  taken  together  are 
called  a  thousand.     Thousands  are  writtr  11  t! 

One  thousand,  1,000    Five  thousand,  5,000 


Two  thousand,  ~'/>00 

Thivr  thousand,  3,000 

Four  thousand,  4,000 


Six  thousand,  6,000 

Bem  thousand,  7,OOO 

Eight  thousand,  8,000 


Nine  thousand,  P,000. 

When  four  figures  are  written  top-tin T  to  express  a  number. 
:":-h:uid  iL'im-  expresses  thoutand*,  and  the  other  three 
res  express  hundred*,  tent,  and  0/«s.     Thus, 
8,000  is  eiuht  thousand, 
5,400  is  live  thousind  four  hund: 
'J..1W)  is  two  thousand  five  luindred  siv 
1,644  is  one  thousand  six  li  ur, 

:hnv  thousand  seven  hui 
O/.'-l  iiousund  nine  hundred  forty-two, 

"•  i.-  time  thousand  four  hundred  five, 
4,096  is  four  thousand  ninety-six, 
7,010  is  seven  thousand 
6,000  is  six  thousand  nine. 

15.  Write  in  words  the  following  numbers:  4,000;  6,200; 
2,500;  5,100;  2,460;  4,620;  5,910. 

in  words  8,123;  3,434;  7,090;  1,050. 

16.  Write  in  words  3,091 ;  4,082;  2,075;  6,204;  3,708; 
4,070;  9,030;  9,999. 

:•  .  IAJMVSS  l.y  liirures  six  tliousand.  live  thousand  three 
hundred,  two  tliousand  one  luindred  thirty,  eight 
tliousand  three  hundred  twenty-!: 

.press  by  TILTH  res  four  thousand  fifty,  seven  thou- 
sand two,  nine  thousand  >'  thousand 
two  hundred  seven. 


ADDITION. 


11 


SECTION  II. 


1.  Prom  1  and  1  to  10  and  10. 

(See  Manual,  page  171.) 

.7.  In  this  picture  of  a  picnic  party,  is  a  group  of  boys, 
3  of  whom  arc  standing,  and  2  are  sitting.  How 
many  boys  are  in  the  group  ?  Methods,  page  IM. 

2.  How  many  trees  are  1  tree  and  2  trees  ?    Method*,  page  *7  '4. 

3.  1  girl  and  1  girl  are  how  many  girls  ? 

4.  One  boy  and  four  boys  are  how  many  beys  2 

5.  How  many  men  are  4  men  and  2  men  ? 

G.  How  many  children  are  6  children  and  2  children  ? 
7.  Jane  bought  two  peaches  for  5  cents,  and  some  pea- 
nuts for  1  cent.    How  many  cents  did  she  pay  out  ? 


12  FIRST    COURSE    IX     INTEGERS. 

8.  Alice  bought  a  pr-ar  for  1  cent,   and   a   bun 
grapes  for  7  rants.    How  many  cents  di 

9.  2  balls  and  7  balls  are  how  many  balls  ? 

10.  9  girls  and  1  boy  are  in  the  same  class.    II«>\\ 
pupils  an-  in  the  class? 

11.  William's  father  pave  him  8  marbles,  and  In-  found  1. 
I  low  many  marbles  had  he  tlien? 

1 :.    Bob  rt   paid   in  cent-   f»r  I 

« il.    How  many  cents  did  hi 
cost  him  ? 
IS.  I  low  many  books  arc  9  books  and  2  books? 

Mire-books,  and  5  book-  without  pic- 
tures.    How  many  books  has  B 

iarles  }>aid  1  cents  for  an  orange,  ; 
a  leinMii.      How  much  did  he  pay  for  b- 

i  liree  roses  are  on  one  bush,  and  six  on  an 
How  many  roses  are  there  on  both  bushes  ? 

/..   I  lit  hard  has  3  rabbits,  and  Thomas  has  3.    How 
many  rabbits  have  th<-  two  h. 

/v.  Manila's  muff  cost  \\  dollars,  and  IHT  fur  cape  7 
dollars.     How  much  did  both  of  them  cost? 

ire  are  8  whi  lack  ones. 

How  many  sheep  are  in  the  pastu: 

you  pay  •'>  nuts  for  figs,  and  9  cents  for  ra 
how  many  cents  do  you  pay  out  ? 
.  .'.   Hiram  found  5  e^rs  in  one  nest,  and  4  in  an 

How  many  eggs  did  lie  find? 

;??.  A  hunter  shot  t<  n  pL'.-ons.  an(l  two  quails.    How 
many  birds  did  he  shoot  ?     M,-th<>ti*.  r 

'ora  had  1  shells,  and  her  brother  gave  her  4  more. 
How  many  shells  had  she  then  ? 


ADDITION.  13 

24.  If  a  ball  costs  6  cents,  and  a  top  4  cents,  how  much 
do  both  cost  ? 

25.  A  chandler  sold  4  boxes  of  candles  to  one  grocer, 
and  7  boxes  to  another.   How  many  boxes  did  he  sell 
to  both  ? 

26.  Sarah  is  9  years  old,  and  her  brother  Joseph  is  4 
years  older.     How  old  is  Joseph  ? 

27.  Fanny's  silk  dress  cost  10  dollars,  and  her  bonnet  4 
dollars.     How  much  did  both  cost  ? 

28.  A  hotel  keeper  buys  4  loaves  of  brown  bread,  and  8 
loaves  of  white  bread,  every  day.    How  many  loaves 
of  bread  does  he  buy  daily  ? 

How  many  are 


29.  5  lilies  and  5  lilies  ? 

30.  4  cherries  and  5  cherries  ? 

31.  5  cherries  and  4  cherries  ? 

32.  6  pears  and  5  pears  ? 

33.  5  pears  and  6  pears  ? 


34.  5  days  and  7  days  ? 

35.  7  days  and  5  days  ? 

30.  10  minutes  and  5  minutes  ? 

37.  5  weeks  and  9  weeks  ? 

38.  9  weeks  and  5  weeks  ? 


In  each  of  the  preceding  problems  we  have  united  or  put 
together  two  numbers  to  form  one  larger  number. 

Addition  is  the  process  of  uniting  two  or  more  numbers 
to  form  one  number. 

The  Amount  or  Sum  is  the  result  obtained  by  Addition. 

The  *Parts  are  the  numbers  which  are  united  to  form  the 
sum. 

The  Siffn  of  Addition.,  made  thus,  +  ,  is  called  Plus; 
and  when  written  between  numbers,  it  signifies  that  they  are  to 
be  added. 

The  Siffn  of  Equality >  made  thus,  =,  when  written  be- 
tween numbers  or  sets  of  numbers,  signifies  that  they  are  equal 
to  each  other.  Thus,  5  +  3  +  9  =  17  is  read,  "  5  plus  3  plus 
9  equals  17,"  or  "  the  sum  of  5,  3,  and  9  is  17." 

A  number  with  the  sign  $  before  it  expresses  dollars.  Thus, 
$72  is  read  "72  dollars." 


14:       FIRST  COUBSE  IN  INTEGERS. 

.*'/.   IIo'.v  many  sheep  are  7  sheep  +  3  sh 
40.  5  cows  -f  7  cows  are  how  many  cows  ? 
,}  1.  4  horses  +  7  horses  =  how  many  horses  ? 
42.  What  is  the  sum  of  $7  -f  $7  ?     Of  $7  +  $9  ? 
4S.  8  robins  +  7  robins  =  how  many  robins  ? 
44.  How  man  ;o  7  wrens  +  10  wrennf 

; ".  An    upholsterer  made  the   scats  for  G   mal. 

chairs,  and  6  rosewood  chairs.      How  many  chair 

seats  did  IK-  mak 

\  dairy-man  bought  7  large  milk-pans,  and  r. 

ones.     How  many  milk-pans  did  he  buy  ? 
;,.   Mary  has  0  pinks,  and  Clara  has  C.      How  many 

pinks  have  the  two  girls? 

48.  A  grocer  sold  5  bushels  of  sweet  apples,  a: . 

f  sour  ones.    How  many  bushels  of  both  1. 
did  lu-  | 

;  .   How  many  quarts  of  milk   will   it  take   to  fill  a 
i;-<|iiart  pan  and  an  S-<juart  pail? 

50.  A  sold  a  bracelet  for  $7,  and  a  lock 

$7.      1I..\\   much  did 

.:/.  If  it  tak«-s  7  yards  fora  dress  for  Jo  and  s 

>r  one  f«>  P,  how  many  yards  will  it 

thf  t\vo  dresses? 

.:.'.   ( >  •  millinrr  mad.-  1»>  !>«.!. 

How  many  bonnets  did  she  make  ii 
two 

53.   1   sold    nine   plows   one   day,  and    .- 
II..\v  many  plows  did  I  sell  in  the  two  d 

.    \  hoy  pitliered  Is  of  appl-s  in  the  forenoon, 

and  S  Imshels  in   the  afternoon.     How  many  bush- 
els did  he  gather  in  all  day? 


ADDITION.  15 

55.  If  you  go  8  miles  east,  and  I  go  9  miles  west  from 
this  school-house,  how  far  apart  will  we  be  ? 

56.  A  horse-dealer  bought  9  black  horses,  and  9  bay 
ones.    How  many  horses  did  he  buy? 

57.  A  book-keeper  wrote  9  pages  of  entries  in  the  fore- 
noon, and  10  pages  in  the  afternoon.    How  many 
pages  did  he  write  in  the  day  ? 

58.  I  paid  an  agent  $10  for  insuring  my  dwelling- 
house,  and  $10  for  insuring  my  furniture.    How 
much  did  my  insurance  cost  me  ? 

59.  Add  1  to  1,  2,  3,  4,  5,  6,  7,  8,  9, .and  10,  in  this  manner:  1 
and  1  are  2,  2  and  1  arc  3,  3  and  1  are  4,  and  so  on. 

(See  Manual,  page  171.) 
GO.  Add  2  to  1,  2,  3,  4,  and  so  on  to  19  inclusive. 

61.  Add  3  to  1,  2,  3,  4,  and  so  on  to  10  inclusive. 

62.  Add  4  to  each  number  from  1  to  10  inclusive. 

63.  Add  5  to  each  number  from  1  to  10  inclusive. 

64.  In  the  same  manner,  add  0  to  1,  2>  3,  4,  and  so  on  to  10 
inclusive. 

65.  In  the  same  manner,  add  7  to  1,  2,  3,  4,  5,  6,  7,  8,  9,  and  10. 

66.  Add  8  to  1,  2,  3,  4,  5,  G,  7,  8,  9,  10. 

67.  Add  9  to  1,  2,  3,  4,  5,  G,  7,  8,  9,  10. 

68.  Add  10  to  each  number  from  1  to  10  inclusive. 

2.   Addition,  from  1  and  11  to  10  and  99- 

GO.  A  blacksmith  shod  13  horses  one  day,  and  4  horses 
the  next.  How  many  horses  did  he  shoe  in  the  two 
days? 

70.  The  third  day  he  shod  5  horses.    How  many  horses 
did  he  shoe  in  the  three  days  ? 

71.  Alfred  bought  a  knife  for  45  cents,  and  sold  it  so  as 
to  gain  5  cents.     How  much  did  he  get  for  it  ? 


16  FIRST    COURSE    IN    INTEGERS. 

,  ..  Twcnt  y-five  children  were  in  their  seats  when  school 
opened  in  the  morning,  und  three  afterward  came 
in.  How  many  children  were  in  school  that  d; 

73.  What  is  the  sum  of  $01  and  £ 

74.  My  father  is  38  years  old.    How  old  will  1 


paper-han^vr  used  8  rolls  of  paper  for  a  bedroom, 
and  Ml  mils  for  a  parlor.  How  many  rolls  of  pap.  T 
did  he  use  for  tin-  two  rooms? 

?'<'.  If  I  pay  *\i  1  f.T  a  (-at,  and  $6  for  a  hat,  how  much 
do  I  pay  tor  both? 

milk-man  who  had  18  cows,  b<>ii_'';;  "•  BfcOra  H«\v 
many  cows  had  he  th 

;  ?.  \  boy  tied  a  string  10  yards  long  to  a  k 
yards  long.    How  long  was  the  who 

7ft  Two  fishermen  caught  43  shad  and  7  p' 

one  haul  of  a  seine.  How  many  fish  did  they  catch  ? 

id  I  and  87.     Add  5  and  69. 
,<?/.  What  is  the  sura  of  6  nncl  89?    Of  7  and  84  ? 

^  .'.  II.  nnan's  frrandfailn-r  was  73  years  old  8  years  ago. 
How  old  is  he  now? 

•v-.'.  Chi   a   ferry-l»»at   were  -1(5  peiitlrnicii  and    10  ladies. 
How  many  passengers  were  on  board  ? 

84.  Th-1    Brew   <»f  the  boat  consisted  of  8  men.     How 
many  persons  were  on  board  ? 

.A  fann.-r  paid  $54  for  a  grain  drill,  and  $9  f.>r  a 
plow.     I  low  much  did  he  pay  for  both  ? 

86.  A  laborer  who  had  $50  in  the  savinirs-hauk,  dcpos- 
d  $8  more.     How  much  money  had  he  then  «  n 
deposit  ? 


ADDITION.  17 

S7.  There  were  96  logs  in  the  river  near  a  saw-mill, 
and  7  on  the  river  bank.  How  many  logs  were  there 
in  all? 

88.  A  lady   bought  9  yards  of  hall  carpeting,  and  37 
yards  of  parlor  carpeting.    How  many  yards  of  car- 
peting did  she  buy  ? 

89.  One  forenoon  I  traveled  69  miles  by  railroad,  and  7 
miles  by  stage.  How  far  did  I  travel  that  forenoon  ? 

90.  In  the  afternoon  I  walked  6  miles.     How  far  did  I 
travel  that  day  ? 

01.  A  farmer  has  98  acres  of  cleared  land,  and  8  acres 
of  woodland.  How  many  acres  are  there  in  his  farm  ? 
9$.   83  +  9  =  how  many  ?     9  +  37  =  how  many  ? 

3.  Addition  by  Decades,  or  Skips  of  Ten. 

.      /. 

93.  Add  1  to  10,  20,  30,  40,  50,  60,  70,  80,  and  90. 

(See  Manual,  page  171.) 

94.  What  is  the  sum  of  11  and  1?     21  and  1?     31  and  1? 
41  and  1  ?    51  and  1  ?    61  and  1  ?     71  and  1  ?     81  and  1  ? 

91  and  1  ? 

95.  What  is  the  sum  of  12  and  1  ?     22  and  1  ?    82  and  1  ?    42 
and  1  ?     52  and  1  if     62  and  1  ?      72  and  1  ?      82  and  1  ? 

92  and  1  ? 

96.  How  many  are  13  and  1  ?    23  and  1  ?     33  and  1  ?    43 
and  1  ?    53  and  1  ?    63  and  1  ?     73  and  1  ?     83  and  1  ? 

93  and  1  ? 

97.  How  many  arc  14  and  1  ?     24  and  1  ?     34  and  1  ?    44 
and  1  ?     54  and  1  ?    64  and  1  ?     74  and  1  ?     84  and  1  ? 

94  and  1  ? 

98.  How  many  are  15  and  1  ?     25  and  1  ?     35  and  1  ?    45 
and  1  ?     55  and  1  ?     65  and  1  ?     75  and  1  ?     85  and  1  ? 

95  and  1  ? 

90.   Add  1  to  16,  26,  36,  46,  56,  66,  76,  86,  and  96. 

2 


18  FIBST    COURSE    IX    INTI.uKRS. 

100.  Add  1  to  17,  27,  :J7,  47.  ;,  87,  and 

101.  Add  1  to  18,  28,  38,  48,  58,  68,  78,  88,  and  98. 

1    ..    What  is  the  sura  of  19  and  1  ?     29  and  1  ?     39  and  1  ? 
49  and  1  ?    59  and  1  ?     69  and  1  ?    79  and  1  ?    81- 

1  ?    99  and  1? 

o 

•v    . 

103.   Add  2  to  10,  20,  30,  40,  50,  60,  70,  80,  and  00. 

Add  2  to  every  tenth  number  from  11  to  91  inclu 

105.  Add  2  to  12,  22,  82,  and  so  on  to  92  inclusive. 

106.  How  many  are  13  and  2  ?     23  and  2  ?     33  and  2  ?    43 
and  2?     53  and  2?     63  and  2  ?     73  and  2  ?     83  an 

;id  2? 

How  many  are  14  and  2?    24  and  2?    34  and  2  ?    44 
and  2?     54  and  2?     64  and  :       74  and  2  ?     *4  an- 

10S.  How  many  are  15  and  2  ?    25  and  2?    85  • 

I  ?    65  and  2  ?     75  and  2  ?    85  an 

100.   Add  2  to  16,  26,  36,  46,  56,  66,  76,  86,  and  9«. 
110.   Add  2  to  17,  27,  37,  47,  57,  67,  77,  87,  and  97. 
///.    Add  2  to  18,  28,  38,  48,  58,  68,  78,  88,  and  98. 
lit.   What  is  the  sum  of  19  and  2  ?     29  and  2  ?     89  and  2  ? 
49  and  2  ?    59  and  2  ?    69  and  2  f     79  and  2  ?    80 

J-. 

113.   Add  3  to  every  tenth  number  from  10  to  90  i 
ll'f.    Add  3  to  every  tenth  numluT  from  11  to  91  D 

Add  3  to  .'.  and  so  on  to  92  inclusi . 

//<:.    A. Id  3  to  \:\.  •::',.  :',:!.  4:J,  58,  63,  73,  83,  and  98. 
\dd  3  t.)  14.  M,  :u.  n.  M,  M,  M,  s4,  and  94. 
IW.  Add  3  to  15,  25,  35,  45,  55,  65,  75,  85,  and  95. 

1  96. 

\  Id  :]  to  17.  27.  37.  47.  r.T  7.  and  97. 

121.   Add  8  to  18,  28,  88,  48,  58,  68,  78,  88,  and  98. 
199.  Add  3  to  1"  M,  7  '   W.  H 


ADDITION.  19 


123.  Add  4  to  every  tenth  number  from  10  to  90  inclusive. 

124.  Add  4  to  every  tenth  number  from  11  to  91  inclusive. 

125.  Add  4  to  12,  22,  32,  and  BO  on  to  92  inclusive. 

126.  Add  4  to  13,  23,  33,  43,  53,  63,  73,  83,  and  93. 

127.  Add  4  to  14,  24,  34,  44,  54,  64,  74,  84,  and  94. 

128.  Add  4  to  15,  25,  35,  45,  55,  65,  75,  85,  and  95. 

129.  Add  4  to  16,  26,  36,  and  so  on  to  96  inclusive. 

130.  Add  4  to  every  tenth  number  from  17  to  97  inclusive. 

131.  What  is  the  sum  of  18  and  4  ?     28  and  4  ?     38  and  4  ? 
48  and  4  ?     58  and  4  ?     68  and  4  ?    78  and  4  ?     88  and 
4  ?     98  and  4  ? 

132.  Add  4  to  19,  29,  39,  49,  59,  69,  79,  89,  and  99. 

5. 

133.  Add  5  to  every  tenth  number  from  10  to  90  inclusive. 

134.  Add  5  to  11,  21,  31,  41,  51,  61,  71,  81,  and  91. 

135.  Add  5  to  every  tenth  number  from  12  to  92  inclusive. 

136.  Add  5  to  every  tenth  number  from  13  to  93  inclusive. 

137.  Add  5  to  14,  24,  34,  and  so  on  to  94  inclusive. 

138.  Add  5  to  15,  25  35,  and  so  on  to  95  inclusive. 

139.  Add  5  to  16,  26,  36,  and  so  on  to  96  inclusive. 

140.  Add  5  to  every  tenth  number  from  17  to  97  inclusive. 

141.  What  is  the  sum  of  18  and  5  ?     28  and  5  ?     38  and  5  ? 
48  and  5  ?    58  and  5  ?    68  and  5  ?    78  and  5  ?    88  and  5  ? 
98  and  5  ? 

142.  Add  5  to  19,  29,  39,  and  so  on  to  99  inclusive. 

6. 

143.  Add  6  to  10,  20,  30,  and  so  on  to  90  inclusive. 

144.  Add  6  to  11,  21,  31,  and  so  on  to  91  inclusive. 

145.  Add  6  to  every  tenth  number  from  12  to  92  inclusive. 

146.  Add  6  to  every  tenth  number  from  13  to  93  inclusive. 

147.  Add  6  to  14,  24,  34,  and  so  on  to  94  inclusive. 


20      FIRST  COUBSE  IN  INTEGERS. 

148.  Add  6  to  15,  25,  35,  and  so  on  to  95  inch; 

149.  Add  6  to  16,  20,  30,  and  so  on  to  90  inclusive. 

150.  Add  C  to  cvcrj-  tenth  number  from  17  to  97  inclusive. 
l.'l.  What  i*  the  sum  of  18  and  0  ?     28  and  6  ?     88  and  0  ? 

48  and  0  ?     58  and  6  ?    68  and  6  ?     78  and  6  ?     88  and 
6  ?     98  and  6  ? 
153.   Add  6  to  19,  29,  89,  and  so  on  to  99  inclusive. 


153.   Add  7  to  10,  20,  30,  and  so  on  to  90  in 

AM.l  7  to  11,  21,  81,  and  so  on  to  91  inclusi 

155.   Add  7  to  12,  22,  32,  42,  52,  I  and  92. 

Add  7  to  every  tenth  number  from  13  to  93  inclusive. 
\«ld  7  to  14,  24,  84,  and  so  on  to  94  inclusive. 

158.  Add  7  to  r..  K,  :«,  and  BO  on  to  95  inclusive. 

159.  Add  7  to  16,  26,  86,  and  so  on  to  90  inclusive. 
1GO.   Add  7  to  17.  27.  37,  and  so  on  to  97  inclusive. 

161.  Add  7  :  h  number  from  18  to  98  inclusive. 

162.  How  many  are  19  and  7  ?    29  and  7?    89  and  7  ?    49 
•ad  71    59  and  7?    69  and  7  ?    79  and  7?    89  an 

99  an.l  7  ' 

8. 

163.  Commencing  at  10,  add  8  to  every  t  nth  number  to  90 
inclu 

164.  Commence  at  11,  and  add  8  to  every  tenth  number  to 
91  inclu.- 

Add  8  to  12,  22,  32,  i 0  '.  b2,  and  92. 

166.   Add  8  to  13,  23,  83,  and  so  on  to  93  inclu -i . 

Add  8  to  every  tenth  number  from  14  to  94  inclusive. 
168.    Add  8  to  every  tenth  numlier  from  15  to  95  inclusive. 

!  low  many  are  1C  and  8  ?    26  and  8  ?    36  and  8  ?    46  and 

8  ?    56  and  8  ?    60  and  8  ?    76  and  8  ?    86  and  8  ?     96 

and  8? 
170.   Add  8  to  17,  27,  87,  and  so  on  to  97  inclusive. 


ADDITION.  1 

171.  Add  8  to  every  tenth  number  from  18  to  98  inclusive. 

172.  How  many  are  19  and  8  ?     39  and  8  ?     39  and  8  ?    49 
and  8?    59  and  8?     69  and  8?     79  and  8?     89  and  8? 
99  and  8  ? 

9. 

173.  Add  9  to  every  tenth  number  from  10  to  90  inclusive. 

174.  Add  9  to  11,  21,  31,  41,  51,  61,  71,  81,  and  91. 

175.  Commence  at  12,  and  add  9  to  every  tenth  number  to 
92  inclusive. 

176.  Add  9  to  13,  23,  33,  and  so  on  to  93  inclusive. 

177.  Add  9  to  every  tenth  number  from  14  to  94  inclusive. 

178.  Add  9  to  every  tenth  number  from  15  to  95  inclusive. 

179.  How  many  arc  16  and  9  ?    26  and  9  ?    36  and  9  ?    46  and 

9  ?     56  and  9  ?     66  and  9  ?     76  and  9  ?     86  and  9  ?     96 
and  9? 

ISO.   Add  9  to  17,  27,  37,  and  so  on  to  97  inclusive. 

18 1.  Add  9  to  every  tenth  number  from  18  to  98  inclusive. 

182.  Add  9  to  every  tenth  number  from  19  to  99  inclusive. 

w. 

183.  Add  10  to  every  tenth  number  from  10  to  90  inclusive. 

184.  Add  10  to  11,  21,  31,  and  so  on  to  91  inclusive. 

185.  Add  10  to  12,  22,  32,  and  so  on  to  92  inclusive. 

186.  Add  10  to  13,  23,  33,  43,  53,  63,  73,  83,  and  93. 

187.  Add  10  to  every  tenth  number  from  14  to  94  inclusive. 

188.  Add  10  to  every  tenth  number  from  15  to  95  inclusive. 

180.  How  many  arc  16  and  10  ?     26  and  10  ?    36  and  10  ?    46 
and  10?     56  and  10?     66  and  10?     76  and  10?     86  and 

10  ?     96  and  10  ? 

190.  Add  10  to  17,  27,  37,  and  so  on  to  97  inclusive. 

191.  Add  10  to  every  tenth  number  from  18  to  98  inclusive. 

192.  Add  10  to  every  tenth  number  from  19  to  99  inclusive. 

(Sec  Manual,  page  171.) 


FIRST  COURSE  IN  INTEGERS. 


SECTION  III. 

A  US  TEA  C  TJ  OJV. 
4.  Prom  1  minus  1  to  20  minus  10. 

WE  can  see  3  ,,f  th<  windows  of  this  school-house; 
1  of  them  is  small,  and  the  others  are  large.  How 
many  large  windows  can  we  see  ?  Mfthod*,  p«gr  /;  /. 

1  tree  from  2  trees  leaves  how  many  trees  I 

OIK    <>f  til-*  four  girls  in  the  yard  is  sitting  < 
and  the  others  are  at  play.     I  low  many  art 

2  hoys  from  2  lioys  leave  how  many  boys? 

In  the  street  are  4  children  at  play,  and  0  <,f 
boys.    How  many  are  girls  ?    Method*,  poo. 
2  marhlc*  from  .3  m.irhles  leave  how  many  marbles? 
I  hoop  from  1  hoop  leaves  how  many  hoops? 
Then-  an*  :»  school  clays  in  1  week     If  Julius  is  ab- 
•?  day-;,  how  many  days  is  he  in  scL 

Florence  brought  7  roses  to  school,  and 
them  to  her  teacher.    How  many  had  she  i 


SUBTBACTIOtf.  23 

10.  In  a  pasture  were  9  horses,  but  1  of  them  jumped 
out.    How  many  remained  in  the  pasture  ? 

11.  Otis  had  7  doves,  hut  2  of  them  have  died.    How 
many  has  he  now  ?     Methods,  page  174. 

12.  A  girl  bought  some  steel  pens  for  2  cents,  and  gave 
in  payment  a  10-cent  piece.     How  many  cents  in 
change  did  she  receive  ? 

U.  Eliza  is  11  years  old,  and  Hannah  is  2  years  younger. 
How  old  is  Hannah  ? 

14.  A  silversmith  made  12  butter  knives,  and  sold  all 
but  2  of  them.    How  many  did  he  sell  ? 

!•').  4  boys  were  skating,  but  3  of  them  went  home. 
How  many  then  remained  on  the  ice  ? 

16.  A  cabinet  maker  made  5  tables,  and  sold  3  of  them. 
How  many  had  he  left  ? 

11.  On  a  pear  tree  were  8  pears,  but  Julia  picked  3  of 
them.    How  many  were  left  on  the  tree  ? 

18.  Seven  carpenters  commenced  building  a  house,  but 
five  of  them  left.     How  many  remained  ? 

19.  A  man  earns  10  dollars  in  a  week,  and  his  son  earns 
3  dollars.  How  much  more  does  the  father  earn  than 
the  son  ? 

20.  If  a  dress-maker  earns  $12  in  a  week,  and  expends 
$3,  how  much  does  she  save  ? 

2L  A  farmer  having  6  calves,  sold  4  of  them  to  a 
butcher.    How  many  had  he  left  ? 

22.  Irene  had  8  canary-birds,  but  5  of  them  escaped. 
How  many  had  she  then  ? 

23.  A  tinsmith  made  13  pails,  and  sold  4  of  them.  How 
many  remained  unsold  ? 


•.M  ruisT  co  UK  si:   i ::   INTEGERS. 

24.  One  morning    • 

re   lying  at  a  wharf, 
but  during  the  day  4  of 

thrill  sailed  away.     II<>w 
many \  I  the 

wharf  at  night? 

25.  No  vessels  from  four  vessels 
leave  how  many  vessels? 

26.  A  Mak.  T  made  9  baskets,  4   «>f   tlum  of 
si>]'  1    the   others  of   willow.      How   m 

Willow  1  lid   lie  111;;' 

.,.    I  paid  a  >\\\>  r-mith  $11  for  a  cak*.-  basket,  and  $4 
less  for  a  set  of  tea-spoons.     How  much  di«l 
spoons  cost  ni'  ? 

u'li  of  the  preceding  problems  w 
two  numhers  from  another  to  timl  the  difference. 

Xtib/rfirfitt/i  -cess  of  taking  one  of  two  numbers 

from  tin-  i •• 

The  'tinndimlcr  or    />ijj'<  / 
sul  fraction. 

The  .iffnurtHl  is  th:it  one  of  two  numbers  from  wh; 
other  is  to  be  taken. 

The  XithfrttJu-tnl  i>  that  one  of  two  numbers  which  is  to 
be  takt  n  from  the  other. 

The    Xi*/n   <>f  .s'//  /,    made    thus,   — ,    is    < 

Minus;  and  when  written  between  two  numbers,  it  signifies 
that  the  number  arter  it  is  to  be  suhtruete  1  from  the  number 
before  it.  Thus,  ir,  -  C  is  read,  '  !•"»  minus  6,"  and  signifies 
that  0  is  to  be  subtracted  from  15. 

low  many  are  10  sheep  —  8  sheep  ? 
89.   12  cows  —  5  cows  =  how  many  cows  ? 

AVh.it  is  the  difTerei;  \\  11  horses  and  4  horses? 

The  minuend  is  9  and  the  subtrahend  is   1.     What  is  the 
remainder  ? 


SUBTRACTION.  25 

32.  A  wood  dealer  sold  6  cords  of  wood,  from  a  pile  of 
7  cords.     How  many  cords  were  left  in  the  pile  ? 

33.  A  boy  sold  a  water-melon  for  8  cents,  and  a  bunch 
of  grapes  for  6  cents.     How  much  more  did  he  get 
for  the  melon  than  for  the  grapes  ? 

34'  A  man  bought  9  pounds  of  butter,  and  his  family 
used  6  pounds  of  it  in  a  week.  How  many  pounds 
were  left  ? 

35.  There  are  G  passengers  in  a  stage-coach,  which  has 
seats  for  15  passengers.    IIov/  many  vacant  seats  are 
there  in  the  coach  ? 

36.  A  soldier's  monthly  pay  is  813.     If  he  spends  86, 
how  much  does  he  save-? 

37.  Of  the  1C  schools  in  a  certain  town,  G  are  taught 
by  gentlemen.    How  many  are  taught  by  ladies  ? 

38.  One  Saturday  7  boys  and  7  girls  were  skating.  How 
many  more  boys  than  girls  were  there  ? 

39.  James  has  9  rabbits ;  7  of  them  are  gray,  and  the 
others  are  white.      How  many  white  rabbits  has 
he? 

40.  In  traveling  12  miles,  I  rode  7  miles,  and  walked 
the  remainder  of  the  distance.   How  many  miles  did 
I  walk  ? 

41.  The  minuend  is  14,  and  the  subtrahend  is  7.     What  is  the 
difference  ? 

4?,.  A  merchant  has  two  clerks.    To  the  older  one  he 

pays  816  a  month,  and  to  the  younger  one  87  less. 

How  much  are  the  monthly  wages  of  the  younger 

clerk? 
43.  A  farmer  having  15  cows,  sold  7  of  them.      How 

many  did  he  keep  ? 


26  FIRST    COURSE    IX    INTEGERS. 

44.  Of  the   17  cars  of  a  freight  train,  7  are  empty. 
How  many  are  loaded  ? 

45.  Of  the  loaded  cars  7  contain  grain,  and  the-  others 
flour.     llo\v  many  cars  contain  flour  ? 

46.  7  and  how  many  arc  11  ?      Methods,  page  174. 

47.  Nelson  is  12  years  old.    How  old  was  h<  •  1  y.  ars  ago  ? 

48.  Andrew  has  caught  8  trout,  and  Louis  8.     Which 
has  caught  the  greater  number  ? 

:  .  I  Tow  many  more  must  Andrew  catch  to  haw  II  ? 

How  many  more  to  have  15  ? 
50.  Which  is  the  greater,  13  —  8  or  14  —  9  ? 

\  gun.-mith   made  10  rifles,  and  sold  8  of  them. 
How  many  remained  unsold  ? 

52.  8  and  how  many  are  18  f 

53.  A  gardener  carried  17  bushels  of  green  peas  t<>  the 
city.      II.    sold  8  bushels  on  First  Street,  and 
remainder  on  Second  Street    How  man\ 

did  he  sell  on  Second  Street? 

54*   8  and  how  many  are  18  ?     10  and  how  many  are  18  ? 
How  many  arc  18  less  9  ?     17  less  10  ? 
i  ;xkc  18  minus  10  from  18  minus  8. 

f  tin-  length  of  a  barber's  pole  are  above 
the  ground,  and   the   pole  is  15  feet  long.     How 

much  of  the  pole  is  in  tin-  ground  ? 

58.  One  day  a  newsboy  sold  19  morninir  id  10 
evening  papers.     How  many  more  morning  than 
evening  papers  did  he  sell  ? 

59.  A  blacksmith  bought  10  tons  of  coal,  and  li 
used  9  tons  of  it    How  much  coal  has  lie  1 


SUBTRACTION.  27 

60.  Seven  dollars  have  been  paid  on  a  note  for  nineteen 
dollars.     How  much  remains  due  ? 

61.  How  old  were  you  5  years  ago  ? 

62.  A  farmer  paid  $16   for  a  corn-planter,  and  after 
using  it  two  seasons,  sold  it  for  $9.     How  much  did 
the  use  of  it  cost  him  ? 

63.  13  boys  entered  school  afc  the  beginning  of  the  win- 
ter term,  and  8  of  them  continued  in  school  all  the 
term.  How  many  left  school  before  the  term  closed  ? 

64.  A  potter  made  17  two-gallon  jugs,  and  9  one-gallon 
jugs.    Of  which  kind  did  he  make  the  greater  num- 
ber, and  how  many  ? 

65.  Subtract  1  from  1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  and  11,  in  this 
manner:  1  from  1  leaves  0,  1  from  2  leaves  1,  1  from  3 
leaves  2,  1  from  4  leaves  3,  and  so  on.    (See  Manual,  page  172.) 

66.  Subtract  2  from  2,  3,  4,  5,  C,  7,  8,  9,  10,  11,  and  12. 

67.  Subtract  3  from  3,  4,  5,  6,  7,  8,  9,  10,  11,  12,  and  13. 

68.  Subtract  4  from  4,  5,  6,  7,  and  so  on  to  14  inclusive. 

69.  Take  5  from  5,  6,  7,  8,  and  so  on  to  15  inclusive. 

70.  Take  G  from  6,  7,  8,  9,  and  so  on  to  16  inclusive. 

71.  How  many  are  7  minus  7  ?     8  minus  7  ?     9  minus  7  ? 

10  minus  7  ?     11  minus  7  ?     12  minus  7  ?     13  minus  7  ? 

14  minus  7  ?     15  minus  7  ?     16  minus  7  ?     17  minus  7  ? 

72.  How  many  are  8  minus  8  ?    9  minus  8  ?     10  minus  8  ? 

11  minus  8  ?     12  minus  8  ?     13  minus  8  ?     14  minus  8  ? 

15  minus  8  ?     16  minus  8  ?     17  minus  8  ?     18  minus  8  ? 

73.  What  is  the  remainder,  after  taking  9  from  9  ?     9  from  10  ? 
9  from  11  ?    9  from  12  ?    9  from  13  ?    9  from  14  ?    9  from 
15  ?     9  from  16  ?     9  from  17  ?     9  from  18  ?     9  from  19  ? 

74.  How  many  are  10  —  10  ?    11  —  10  ?    12  —  10  ?    13  —  10  ? 
14-10?      15-10?      16-10?      17-10?      18-10? 
19-10?      20-10? 


28  FIRST    COURSE    IN    INTEGERS. 

5.  Subtraction,  from  20  minus  1  to  110  minus  10. 

77.   Homer  having  2G  rabbits,  sold  5  of  them.      How 
many  had  he  lei 

76.  A  farmer  had  87  sheep,  but  3  of  them  were  killed 
by  dogs.     How  many  sheep  had  he  K  ; 

77.  A  man  bought  a  watch  for  $59,  and  sold  it  for  $9 
less  than  cost    How  much  did  he  get  for  it  '; 

78.  From  a  farm  of  89  acres,  tin-  owner  s. 
How  many  acres  had  he  then  ? 

79.  There  were  20  roses  on  a  bush,  and  Kmik  \ 
8  of  them.    How  many  were  left  on  the  bu 

80.  A  market  woman  took  3G  geese  t  d  sold 

all  but  7  of  them.     How  many  did  she  .- 

81.  A  stove  dealer  sold  a  stove  for  $23,  and  his   pr.-iit 
was  $4.     How  much  did  the  stove  cost  him  !' 

I  gain  $6  by  selling  a  lumber  wagon  for  $91,  h«»\v 
much  did  it  cost  m    ? 

race  is  9  years  old,  and  ht-r  father  is  !."».     What  is 
the  diUcremv  in  their  ages? 

«>ma  pile  containing  '-M  cords  of  wood,  a  tea; 
drew  6  cords.     How  much  wood  was  left  in  the 

pil 

cloth  CO  yards  long,  .-hrank  ;!  yard-  in 
fulling.     What  was  its  length  tin -n  ? 

86.  A  man  having  $36,  paid  $8  for  a  silk  hat.     ll«>w 
much  money  had  lu-  : 

rom  a  cask  containing  :>3  gallons  <>f  oil,  0  gallons 
were  drawn.     How  much  oil  was  left  in  the  cask  ? 

88.  Of  43  guests  who  dined  at  a  hotel, 

many  w.-re  g«-ntl.  in.-n  ? 


SUBTRACTION.  29 

89.  I  have  840.    If  I  pay  $5  that  I  owe,  what  sum  shall 
I  have  left? 

90.  What  ia  the  difference  between  31  and  8  ? 

91.  The  minuend  is  42,  and  the  subtrahend  is  7.     What  is 
the  difference  ? 

92.  Which  is  the  greater,  54  —  9  or  49  —  6  ?  Methods,  p.  l?4. 

OS.  A  cooper  made  100  barrels,  and  5  of  them  were 
condemned  as  bad.  How  many  were  good  ? 

04.  Of  the  good  ones,  7  were  pork  barrels,  and  the 
remainder  were  flour  barrels.     How  many  were 
flour  barrels  ? 

05.  After  selling  8  flour  barrels,  how  many  had  he 
left? 

06.  From  a  chest  containing  82  pounds  of  tea,  a  grocer 
sold  5  pounds.     How  much  tea  was  left  in  the 
chest? 

07.  From  a  coil  of  rope  76  feet  long,  a  piece  9  feet  long 
was  cut.    What  was  the  length  of  the  remainder 
of  the  coil  ? 

98.   Which  is  the  greater,  102  —  9  or  100  —  7  ? 

00.  The  distance  from  A  to  B  is  105  miles  by  canal, 
and  8  miles  less  by  railroad.  What  is  the  distance 
by  railroad  ? 

100.  A  crockery  dealer,  on  opening  a  case  containing 
108  fruit  cans,  found  9  of  them  broken.    How 
many  were  whole  ? 

101.  After  selling  8  of  the  perfect  cans,  how  many  had 
he  left? 

102.  Harry  having   78  cents,   spent  9   cents  for  fire- 
crackers.    How  much  money  had  he  then  ? 


30  FIllST    COUBSE    IX    INTEGERS. 

6.  Subtraction  by  Decades,  or  Skips  of  Ten. 
/. 

103.  Subtract  1  from  10,  20,  80,  40,  50,  60,  70,  80, 90,  and  100. 

(See  Manual,  p*^ 

104.  What  is  the  remainder,  after  taking  1  from  11  ?     1  from 
21  (     1  from  31  i     1  from  41  ?     1  from  51  ?     1  from 

1  from  71  ?     1  from  81  ?     1  from  91  ? 

105.  What  is  the  remainder,  after  taking  1  from  12  ?     1  from 

'.     1  from  32  ?     1  from  42  ?     1  from  52  ?     1  from  62  ? 

1  from  72  ?     1  from  82  ?     1  from  92  ? 

106.  Subtract  1  from  13.  23,  83,  and  so  on  to  98  inclu^ 

107.  Subtract  1  from  14,  24,  34,  and  so  on  to  94  i 

108.  Subtract     from  15,  25,  85,  and  so  on  to  (.r,  iiu  lu 
100.   Subtract     from  16,  26,  86,  46,  56,  66,  76,  86,  and  96. 

110.  Subtract     from  17,  27,  87,  47,  57,  67,  77,  87,  and  97. 

11 1.  Subtract     from  18,  28,  88,  48,  58,  68,  78,  88,  and  98. 
11*.   Subtract     from  19,  29,  89,  and  so  on  to  99  inclu.-! 

2. 

US.   Subtract  2  from  10,  20,  30,  40,  50,  60,  70,  80,  90,  and  100. 

114.  Subtract  2  from  every  tenth  number  from   11  : 
inclusive. 

115.  Subtract  2  from  12,  22,  82,  and  so  on  to  92  inclu> 

116.  What  is  the  remainder,  after  taking  2  from  l: 

23  ?     2  from  33  ?     2  from  43  ?     2  from  53  ?     2  from  63  ? 

2  from  78  ?     2  from  83  ?    2  from  93  \ 

117.  Take  2  from  14,  24,  84,  and  so  on  to  94  inclusive. 

118.  Take  2  from  15,  25,  85,  and  so  on  to  95  inclusive. 
m   Subtract  2  from  16,  26,  86,  46,  56,  66,  76,  86,  and  96. 
ISO.   Subtract  2  from  17.  7.  57,  67,  77,  87,  and 

121.  Sul -tract  2  from  18,  28,  88,  48,  58,  68,  78,  88,  and  98. 

122.  What  is  the  remainder,  after  takin-  2  from  19?     2  from 
29?    2  from  39?     2  from  49  ?    2  from  59  ?    2  from  69  ? 
2  from  79  ?     2  from  89  ?     2  from  99  ? 


SUBTRACTION.  31 

3. 

123.  Subtract  3  from  every  tenth  number  from   10  to  100 
inclusive. 

124.  Subtract  3  from  every  tenth  number  from  11  to  101 
inclusive. 

125.  Subtract  3  from  12,  22,  32,  and  so  on  to  102  inclusive. 

126.  Subtract  3  from  13,  23,  33,  43,  53,  63,  73,  83,  and  93. 

127.  Subtract  3  from  14,  24,  34,  44,  54,  64,  74,  84,  and  94. 

128.  Subtract  3  from  15,  25,  35,  45,  55,  65,  75,  85,  and  95. 
120.   Subtract  3  from  16,  26,  36,  46,  56,  66,  76,  86,  and  96. 
ISO.   Subtract  3  from  17,  27,  37,  47,  57,  67,  77,  87,  and  97. 

131.  Subtract  3  from  18,  28,  38,  48,  58,  68,  78,  88,  and  98. 

132.  Subtract  3  from  19,  29,  39,  49,  59,  69,  79,  89,  and  99. 

£. 

133.  Subtract  4  from  every  tenth  number  from   10  to  100 
inclusive. 

134.  Subtract  4  from  every  tenth  number  from  11  to  101 
inclusive. 

135.  Subtract  4  from  12,  22,  32,  and  so  on  to  102  inclusive. 

136.  Subtract  4  from  13,  23,  33,  43,  53,  63,  73,  83,  93,  and  103. 

137.  Subtract  4  from  14,  24,  34,  44,  54,  64,  74,  84,  and  94. 

138.  Subtract  4  from  15,  25,  35,  45,  55,  65,  75,  85,  and  95. 
130.   Subtract  4  from  16,  26,  36,  and  so  on  to  96  inclusive. 

140.  Subtract  4   from   every  tenth  number  from   17   to   67 
inclusive. 

141.  What  is  the  remainder,  after  taking  4  from  18  ?    4  from 
28  ?    4  from  38  ?    4  from  48  ?     4  from  58  ?     4  from  68  ? 
4  from  78  ?    4  from  88  ?     4  from  98  ? 

142.  Subtract  4  from  19,  29,  39,  49,  59,  69,  79,  89,  and'  99. 

5. 

143.  Subtract  5  from  10,  20,  30,  40,  50,  60,  70,  80,  90,  and  100. 
144-   Subtract  5  from  11,  21,  31,  41,  51,  61,  71,  81,  91,  and  101. 
145.   Subtract  5  from  every  tenth  number  from   12  to  102 

inclusive. 


32      II  KST  COURSE  IN  1NTEGEBS. 

146.  Subtract  5  from  every  tenth   number  from  13  to  103 
inclu 

147.  Subtract  5  from  14,  24,  34,  44,  54,  64,  74,  84, 94,  and  104. 

148.  Subtract  5  from  1",,  2.~>,  35,  and  so  on  to  95  inch; 

149.  Subtract  5  from  16,  26,  86,  and  so  on  to  96  inch: 

150.  Subtract  5  from  every  tenth  number  from   17  to  97 
inclusive. 

151.  What  is  the  remainder,  after  taking  5  from  18  ?     5  from 
28  ?    5  from  88  ?    5  from  48  ?     5  from  58  ?     5  from  68  ? 

-om78?    5  from  88?    5  from  98? 
Subtract  5  from  19,  29,  89,  and  BO  on  to  99  inclusive. 

(J. 
153.   Subtract  6  from  10,  20,  80,  and  so  on  to  100  inclu 

Subtract  6  from  11,  21,  31,41,  and  so  on  to  101  inclu 
.    Subtract    (i   fn»m   every   tenth   number    from    12   to    H»2 

inclusive. 
166.   Subtract  0  from    c\«-ry  tenth  numlxr  from    13   to  103 

inclusive. 

Subtract  6  from  14,  24,  84,  and  so  on  to  104  inch. 
158.   Subtract  6  from  15,  25,  85,  and  so  on  i  isive. 

Subtract  6  from  16,  26,  86,  and  so  on  to  96  inch: 

160.  Subtract  6  from  every  tenth  number  from   17  to  97 
inch: 

161.  What  is  the  remainder,  after  taking  6  from  18?    6  from 
28?    6  from  88?     6  from  48  ?    6  from  58  ?     6  from  68  ? 
6  from  78?    6  from  88  ?    6  from  98  ? 

162.  Subtract  6  from  19,  29,  39,  and  so  on  to  99  inclusive. 

7. 

163.  Subtract  7  from  10.  20,  30,  and  so  on  to  100  inch: 
,164.    Subtract  7  from  1 1.  21.  Ml,  41,  and  so  on  to  101  inclu 

165.  Subtract  7  from  1  .  ',2.  52.  62,  72.  82.  92.  and 

166.  Subtract  7  from   every  tenth  number  from   13  to  103 
inclusive. 


SUBTRACTION". 


33 


167.   Subtract  7  from  14,  24,  34,  and  so  on  to  104  inclusive. 
108.   Subtract  7  from  15,  25,  35,  and  so  on  to  105  inclusive. 

169.  Subtract  7  from  16,  26,  36,  and  so  on  to  106  inclusive. 

170.  Subtract  7  from  17,  27,  37,  and  so  on  to  97  inclusive. 

171.  Subtract   7  from   every  tenth  number  from   18  to   98 
inclusive. 

172.  What  is  the  remainder,  after  taking  7  from  19  ?     7  from 
29  ?     7  from  39  ?     7  from  49  ?      7  from  59  ?     7  from  69  ? 

7  from  79  ?     7  from  89  ?     7  from  99  ? 

8. 

173.  Commencing  at  10,  subtract  8  from  every  tenth  number 
to  100  inclusive. 

174.  Commence  at  11,  and  subtract  8  from  every  tenth  num- 
ber to  101  inclusive. 

775.   Subtract  8  from  12,  22,  32,  42,  52,  62,  72,  82,  92,  and  102. 

176.  Subtract  8  from  13,  23,  33,  and  so  on  to  103  inclusive. 

177.  Subtract  8  from  every  tenth  number  from   14  to  104 
inclusive. 

178.  Subtract  8  from  every  tenth  number  from  15  to  105 
inclusive. 

170.   What  is  the  remainder,  after  taking  8  from  16  ?     8  from 
26  ?     8  from  36  ?     8  from  46  ?     8  from  56  ?     8  from  66  ? 

8  from  76  ?     8  from  86  ?     8  from  96  ?     8  from  106  ? 

180.  Subtract  8  from  17,  27,  37,  and  so  on  to  107  inclusive. 

181.  Subtract  8  from  every   tenth  number  from   18  to  98 
inclusive. 

182.  Take  8  from  19,  29,  39,  49,  59,  69,  79,  89,  and  99. 

0. 

183.  Subtract   9  from  every  tenth   number  from  10  to  100 
inclusive. 

184.  Subtract  9  from  11,  21,  31,  41,  51,  61,  71,  81,  91,  and  101. 

185.  Commence  at  12,  and  subtract  9  from  every  tenth  num- 
ber to  102  inclusive. 


34  FIRST    COURSE    IN    INTEGERS. 

186.  Subtract  9  from  13,  23,  33,  and  so  on  to  103  inclu 

187.  Subtract  9  from  every  tenth  number  from  14  to  104 
inclusive. 

188.  Subtract  9  from  every  tenth  number  from   15  to  105 
inclusive. 

180.   What  is  the  remainder,  after  taking  9  from  16?     9  from 
26?    9  from  36?    9  from  46  ?    9  from  56  ?    9  from 

9  from  76  ?     9  from  86  ?    9  from  96  ?     9  from  106? 
Mil, tract  9  from  17,  27,  37,  and  so  on  to  107  inch; 

r.>l.   Sul. trad  U  from  every  tenth  number  from  18  to  108 
inchi 

1ft?.   Subtract  9  from  every  tenth  number  from    U»  t«»  i««j 
inclusive. 

fO. 

193.  Subtract  10  from  every  tenth  number  from  10  to  100 
incli; 

194.  Subtract  10  from  11,  21,  81,  and  BO  on  to  101  inclusive. 

195.  Subtract  10  from  12,  22,  82,  and  so  on  to  102  inclusive. 

196.  Subtract  10  from  18,  23,  C3, 43, 53,  68, 73,  88,  93,  and  103. 

197.  Subtract  10  from  every  tenth  number  from  14  to  104 
inch; 

198.  Subtract  10  from  every  tenth  number  from  15  to  105 
inch: 

'-Vhat  U  the  remain. 1-  ikinir  10  from  16?  10  from 

lofromiu;,'    10  from  46?   10  from  56?   10  from  66? 

10  from  76?     10  from  86?     10  from  96?     10  from  106? 
£00.   Sul >tract  10  from  17,  27,  37,  and  so  on  to  107  includTe. 
201.  Subtract  10  from  every  tenth  number  from  18  to  108 

inclusive. 

80$.  Subtract  10  from  every  tenth  number  from  19  to  109 
inclusive. 


REVIEW    PROBLEMS.  35 

SECTION    IV. 


1.  EDWARD  gave  5  cents  for  a  pencil,  4  cents  for  a  cake 
of  rubber,  and  7  cents  for  drawing  paper.     How 
many  cents  did  he  expend  ?     Methods,  page  174. 

2.  A  man  husked  9  bushels  of  corn  in  the  forenoon,  7 
bushels  in  the  afternoon,  and  3  bushels  in  the  even- 
ing.   How  much  corn  did  he  husk  in  all  ? 

8.  Albert  has  6  apples,  Frank  has  8,  and  Edgar  has  5. 
How  many  apples  have  the  three  boys  ? 

4.  In  a  certain  school  there  are  5  pupils  in  the  A  class, 
9  in  the  B  class,  7  in  the  C  class,  and  8  in  the  D 
class.    How  many  pupils  are  in  the  4  classes  ? 

5.  A  wood  dealer  has  26  cords  of  maple  wood,  7  cords 
of  hickory,  9  cords  of  beech,  and  5  cords  of  hemlock. 
How  much  wood  has  he  ? 

6.  37  -f  8  +  9  =  how  many  ? 

7.  What  is  the  sum  of  66,  5,  6,  and  9  ? 

8.  How  many  are  48  +  3  +  6  -f  9  +  4  ? 

9.  Reuben  having  9  peaches,  gave  5  to  Ada,  and  4  to 
Juliet    How  many  has  he  left  ?    Methods,  page  174. 

10.  If  I  have  $17,  and  I  spend  $6  for  pictures,  and  $8 
for  books,  how  much  money  shall  I  have  left  ? 

11.  From  a  bin  that  contained  64  bushels  of  wheat,  10 
bushels  were  taken  at  one  time,  and  3  at  another. 
How  much  wheat  remained  in  the  bin  ? 

12.  A  high  rock  on  the  sea-shore  stands  7  feet  in  the 
water.    If  the  tide  rises  7  feet,  and  afterward  falls  9 
feet,  how  many  feet  of  the  rock  will  be  under  water  ? 

Methods,  page  175. 


36      FIRST  COURSE  IN  INTEGERS. 

15.  A  laborer  earned  $11  one  week,  $6  the  next,  and 
spent  $8  in  the  t  much  money  had 
he  1 

14.  89  +  8  —  5  =  how  many  ? 

r>.  Kiijlit  less  than  ri^hty-eight,  plus  nine,  are  how  many? 

16.  50  —  8  —  8  arc  how  many  ? 

17.  If  I  \\a\\-  75  books,  and  give  away  10  of  thorn,  and 

;-d  1'iiy  7  more,  how  many  books  shall  I  then 
h;r. 

/v.  If  I  owe  $54,  $8,  and  $4,  and  I  pay  all  but  $10,  how 

much  do  1  ] 

I  low  many  more  than  7  is  the  sum  of  91,  5,  and  10  '- 
SO.  84  -  9  -  6  -  7  =  how  many? 
2 1.  87  +  8  +  8  —  9  —  5  are  how  many  ? 

ha\ini:  i:  doves,  sold  6  to  Walter,  5  to  Alvan, 
and  4  to  Luther.    How  many  doves  had  he  ;!i n  ? 

,?.;.  Kalph  had  a  10-cent  piec  .  and  a  5-cent  pure  :  but 
he  has  paid  8  cents  of  his  money  for  a  top,  and  7 
cents  for  marbles.  Uow  many  cents  has  he  K 

24.  A  silversmith  melted  together  25  ounces  of  I 
and  6  of  copp.T.     II<   u-  -1  1  ounces  of  Lfafl  mixture 
t  r  tea-spoons,  8  ounces  for  table-spoons,  ami 
rest  for  forks.    How  much  did  he  use  for  forks  ? 

25.  How  old  were  you  7  years  ago  ?    How  old  wil' 
be  7  years  hei 

26.  In  5  years  Ira  will  1  n  old.     How  old  was  he 
6  years  ago  ? 

27.  Levi  has  9  pears  in  his  hat,  10  in  his  pockets,  and  3 
in  his  hand.    If  he  gives  7  pears  to  his  brother,  and 
5  to  his  sister,  how  many  pears  will  he  hav 


MULTIPLICATION. 


SECTION  V, 

MUZ  TI'PZICATIOJV. 
/•   From  2  times  1  to  10  times  10. 

1.  Itf  each  of  two  wagons  there  is  one  barrel  of  flour. 
How  many  barrels  in  both  wagons  ? 

2.  Two  horses  are  called  a  span.     How  many  horses 
are  there  in  two  spans  ? 

3.  There  are  3  windows  in  one  side  of  a  mill,  and  3  in 
one  end.     How  many  windows  are  in  the  side  and 
end? 

i».  A  wagon  has  4  wheels.     How  many  wheels  have  2 

wagons  ? 
o.  Each  railing  of  a  bridge  has  5  posts.     How  many 

posts  have  the  2  railings? 

6.  A  little  girl  bought  2  sticks  of  cream  candy,  2  of 
lemon,  and  2  of  peppermint.  How  many  sticks  of 
candy  did  she  buy  ? 


38  FIBST    COURSE    IN     I  N  T  11  <;  i:  BS. 

7.  There  are  2  boys  on  one  seat,  2  on  another,  2  on 

anoth.-r,  and  2  on  another.     How  many  bo 
the  4  scats? 

8.  If  you  siii«ly  •>  hours  on  Monday,  2  hours  on 

day.  -,l  1  lours  on  W«  dnesday,  2  hours  on  Thursday, 

iiours  on  Friday,  how  many  hours  will 
study  in 

.''.  How  many  are  1  +  1,  or  2  times  1  ? 
J".  I  low  many  are  2  +  2.  or  2  times  2 1 
7  /.  How  many  arc  3  +  3,  or  2  times  8  f 
If.  How  many  are  4  +  4,  or  2  times  4  ? 
IS.  How  many  are  5  +  5,  or  2  times  5  ? 

::iany  arc  2  +  2  +  2,  or  8  times  2  ? 
i  low  many  are  2  -f  2  -f  2  -f  2,  or  4  times  2  f 
How  much  will  2  barrels  of  flour  cost,  at  $8  a 

barrel  ?       Mrthod*,  page  17 S. 

How  many  days  i  .s? 

.  A  cooper  can  make  10  barrels  in  1  day.   How  many 
can  IK-  make  in  2  days  ? 

/.''.  I  low  much  will  2  papers  of  ground  ]>  \  •]> •  r  cost,  at  9 
Htfl  a  pa]> 

.'".  How  much  will  9  axes  cost,  at  $2  apiece? 

&?.  Two  oxen  are  called  a  yoke.    How  many  oxen  are 
;i  yoke  of  oxen  ? 

.'.'.   Hou   many  clu-rries  are 

thriv  in  ;>  dusters  of  3 

clu-rries  each? 
-.'•>.  IIo\\  many  cherries  are 

there  in  4  such  clusters? 

!Iow  many  in   5  clus- 
ters? 


MULTIPLICATION.  39 

2o.  How  many  roses  are  on 
3  branches,  there  being 
5  roses  on  each  branch  ? 

26.  How  many  buds  are  on 
3  stems  of  a  rose-bush, 
if  there  are  4  buds  on 
each  stem  ? 

27.  How  many  leaves  are  on 

3  branches,  if  there  are  6  leaves  on  each  branch  ? 

28.  A  miller  sold  6  barrels  of  corn  meal,  at  $3  a  barrel. 
How  much  did  he  receive  for  it  ? 

20.  If  a  cow  gives  7  quarts  of  milk  a  day,  how  much 
will  she  give  in  3  days  ? 

30.   How  many  eggs  are  3  times  8  eggs  ?     8  times  3  eggs  ? 
SI.   How  many  stars  are  3  times  1 0  stars  ?     10  times  3  stars  ? 
32.   How  many  trees  are  3  times  9  trees  ?     9  times  3  trees  ? 

In  each  of  the  preceding  problems  we  have  found  the  sum 
of  as  many  times  one  of  the  two  given  numbers  as  there  are 
ones  in  the  other  given  number. 

.Iff/It/ plication  is  a  short  process  for  finding  the  sum  of 
as  many  times  one  of  two  numbers  as  there  are  ones  in  the  other. 

The  'Product  is  the  result  obtained  by  Multiplication. 
The  Factors  are  the  numbers  used  to  obtain  the  product. 

The  Multiplicand  is  that  factor  which  is  to  be  taken  any 
certain  number  of  times. 

The  Multiplier  is  that  factor  which  shows  how  many 
times  the  multiplicand  is  to  be  taken. 

The  Sian  of  Multiplication^  made  thus,  x ,  when 
placed  between  two  numbers,  signifies  that  they  are  to  be 
multiplied  together.  It  is  read  "  times,"  or  "  multiplied  by." 
Thus,  4  x  9  is  read  "  4  times  9,"  or  "  4  multiplied  by  9." 


40  FIRST    COURSE    IN     INTEGERS. 

S3.   The  factors  are  4  and  9.     What  is  the  produ 

nc  multiplicand  is  8,  and  the  multiplier  is  o.     What  is 
the  prod  . 
85.   What  is  the  product  of  5  x  7  peaches  ?    Of  0  x  $3  ? 

\  hat  is  the  product  of  4  x  0  ?     0x4? 
87.   2x7  =  how  many  ?    8x5  =  how  many  ? 

38.  How  much  will  4  primers  cost,  at  4  cents  api' 

••'.''.   II<. u  much  will  r»  pounds  of  rha!  nts  a 

pound  ? 
40.  6  spoons,  forks,  or  knives  are  t-all.-d  a  <rt.     ll..\v 

many  forks  are  tin  n-  in  4  sets? 

.J/.  If  8  acres  of  grass  can  be  cut    with   a  nn>uin«:- 
machine  in  a  day,  how  much  can  lx  rut  in  4  da; 

42.  How  mucli  will  4  l.uf  ralo-robes  cost,  at  *'.» 

43.  If  a  forwarder  loads  4  boats  a  day,  how  many  will 

:  in  7  days? 

44.  If  a  laborer  can  dig  4  bushels  of  potatoes  in  an 
hour,  how  many  bushels  can  he  dig  in  10  hours  ? 

; ',.  Ii  .re  is  5  cents,  how  miu-h  will  5 

ridi-s  r. 

46.  How  many  tea-spoons  an  tlim  in  G  sets? 
ID  visit. •<!  S  jiatiri-- 

lluw  many  visits  did  he  make? 

48.  Tin-  milroad  fan-  from  Cleveland  to  Cincinnati   is 
$7.     What  will  tin-  tickets  for  C  passengers  ( 

49.  On  a  freight -train  are  (\  brakmim,  each  of  whom 
rarns  $9  a  wt    k.     How  much  do  all  of  tluin  earn  ? 

measuring  depths  at  sea,  6  feet  are  a  fathom. 
H«»w  many  IVet  are  there  in  10  fathom 
How  many  days  an-  thm-  in  7  weeks? 


MULTIPLICATION.  41 

52.  How  many  week-days  are  there  in  9  weeks  ? 

JJ.  A  miller  can  pack  8  barrels  of  flour  in  an  hour. 
How  many  barrels  can  he  pack  in  7  hours  ? 

'~>'h  What  is  the  cost  of  a  quarter  of  lamb  that  weighs  7 
pounds,  at  10  cents  a  pound  ? 

55.  If  a  joiner  can  make  8  doors  in  a  week,  how  many 
doors  can  he  make  in  10  weeks  ? 

56.  A  blackberry  girl  sold  10  quarts  of  berries,  at  9  cents 
a  quart     How  much  did  she  get  for  them  ? 

57.  She  bought  9  pounds  of  sugar,  at  9  cents  a  pound. 
How  much  did  it  cost  her  ? 

58.  A  music-teacher  gives  8  lessons  in  a  day.     How 
many  lessons  does  she  give  in  8  days  ? 

59.  Two  men  built  a  stone-wall  in  10  days,  building  10 
rods  each  day.    How  many  rods  long  was  the  wall  ? 

GO.  At  a  certain  sea-port  are  9  pilots,  each  of  whom 
piloted  8  vessels  into  the  harbor  in  one  week.  HoW 
many  vessels  entered  the  harbor  that  week  ? 

61.  Which  is  the  greater,  7  x  9  or  8  x  8  ?   (See  Manual,  page  172.) 

fif,  Multiply  2  successively  by  1,  2,  3,  4,  5,  6,  7,  8,  9,  and  10. 

63.  Multiply  3  successively  by  1,  2,  3,  4,  5,  6,  7,  8,  9,  and  10. 

64.  Multiply  4  successively  by  1,  2,  3,  4,  5,  6,  7,  8,  9,  and  10. 

65.  How  many  are  0  time  5  ?    1  time  5  ?   2  times  5  ?   3  times  5  ? 

4  times  5  ?     5  times  5  ?     G  times  5  ?     7  times  5  ?     8  times 

5  ?     9  times  5  ?     10  times  5  ? 

66.  How  many  are  0  time  6  ?    1  time  6  ?   2  times  6  ?   3  times  G  ? 
4  times  6?   5  times  6  ?    6  times  6  ?   7  times  G  ?   8  times  6? 
9  times  6  ?     10  times  6  ? 

67.  Multiply  7  by  0,  1,  2,  3,  4,  and  so  on  to  10  inclusive. 

68.  Multiply  8  by  0,  1,  2,  3,  4,  and  so  on  to  10  inclusive. 
GO.   Multiply  9  by  each  number  from  0  to  10  inclusive. 
70.  Multiply  10  by  each  number  from  0  to  10  inclusive. 


42  r  i  R8T    OOU  us  i:    i  x    i  - 


SECTION  VI 


8.   Prom  2  in  2  and  ono  half  of  2,  to  10  in  100  and  one 
tenth  of  100. 

/.  If  3  hogsheads  of  sugar  m  for  a  dray, 

how  many  loads  will  u  hogsheads  mak 
.'.   How  many  load^  will  !)  ho^ln-ads  in; 

S.  A  drayman  has  12  hogsheads  to  draw  from  a  fr 
house.    How  many  loads  will  tln-v  inn!. 

"(8**  HMO*!,  p^  17*.) 

4*  At  $3  apiece,  how  many  summer  coats  can  bo 
bought  for  $3  ? 

5.  At  2  cents  apiece,  how  many  peaches  can  you  l.uy 
for  8  cents  ?    Method*,  *>«./<  /  . 

'.  How  many  double  desks  arc  required  to  seat  10 

pupils  ? 

7.  A  coppersmith  gets  three  dollars  apiece  for  m;; 
stove  boilers.    How  many  boilers  must  he  i 
cam  tw  nt  \  -one  dollars? 

8.  C  skates  are-  how  many  p: 


DIVISION.  43 

9.  A  hatter  received  $14  for  wool  hats,  at  $2  apiece. 
How  many  hats  did  he  sell  ? 

10.  18  oxen  are  how  many  yoke  ? 

11.  16  gloves  are  how  many  pairs  ? 

12.  How  many  cents  must  Asa  have,  to  buy  20  marbles, 
if  he  gets  2  for  a  cent  ? 

13.  If  one  coat  can  be  made  from  3  yards  of  cloth,  how 
many  coats  can  be  made  from  18  yards  ? 

lJh  How  many  3-cent  postage  stamps  can  be  bought  for 
24  cents? 

15.  A  farmer  sowed  30  bushels  of  plaster  on  a  field  of 
clover,  sowing  3  bushels  to  the  acre.  How  many 
acres  of  clover  were  there  ? 

1G.  At  $4  a  ream,  how  many  reams  of  letter-paper  can  I 
buy  for  $8  ? 

17.  If  a  family  use  4  pounds  of  butter  in  one  week,  how 
many  weeks  will  20  pounds  last  them  ? 

IS.  If  4  plums  cost  one  cent,  how  many  cents  will  12 
plums  cost  ? 

19.  How  much  will  24  pounds  of  coffee  cost,  at  the  rate 
of  4  pounds  for  a  dollar  ? 

20.  A  canvassing  agent  received  &3G  for  books,  at  $4 
apiece.    How  many  books  did  he  sell  ? 

21.  How  many  horse  shoes  can  a  blacksmith  set  with  33 
nails,  using  8  nails  for  each  shoe  ? 

£?.  If  you  put  8  cows  in  2  yards,  putting  the  eame 
number  into  each  yard,  how  many  cows  will  there 
be  in  one  yard  ?  Method*,  page  17 s. 

23.  In  2  farm-yards  are  4  horses,  an  equal  number  in 
each  yard.  How  many  horses  are  in  one  yard  ? 


44 


FIRST    COURSE     IX     INTEGERS. 


When  any  number  of  thingn  it  separated  or  divided  into  two 
equal  portion*  or  part*,  one  of  the  parts  it  one  half  of  the  uhoU 


One  half  Is  written  }. 

£f.  How  many  are  j  of  4  horses  ?    A  of  8  cows? 

25.  A  farmer  has  6  calves  in  2  yards,  J  of  them  being 
in  each  yard.  How  many  calves  has  he  in  . 

&6.  $  of  2  colts  are  how  many  colts  f 
..   A  farmer  havini:  10  sheep,  put  ±  of  them  into  his 
barn-yard.     How  many  were  in  the  barn-yard  ? 

28.  A  milkman  sold  2  quarts  of  milk  for  K>  cents. 
What  was  the  price  of  a  quart  ? 

."'.  Tt  \!  loaves  of  bread  cost  1C  cents,  how  much  will 
one  loaf  cost  ? 

SO.  If  it  tak<->  1  I  yards  of  car]»--ting  to  cover  2  flights 
of  stairs,  how  many  yards  will  it  take  to  cover  one 
flight  ? 

31.  A  chwse-monger  bought  two  cheeses  for  $18.  How 
much  did  he  pay  apiece  for  them? 


DIVISION.  45 

32.  How  inucli  is  the  fare  from  Detroit  to  Milwaukee, 
if  2  tickets  cost  820  ? 

83.  If  I  divide   6  pears  equally  among  3   girls,  how 
many  pears  will  each  girl  have  ? 

34.  If  4  boys  together  gather  8  quarts  of  chestnuts,  how 
many  quarts  arc  there  in  each  boy's  share  ? 

When  any  number  of  tilings,  ones,  or  units  is  divided  into  three 
equal  parts,  one  part  is  one  third  of  the  number  divided;  and 

When  any  number  of  things,  ones,  or  units  is  divided  into  four 
equal  parts,  one  part  is  one  fourth  of  the  number  divided. 

One  third  is  written  ^ ;  and  one  fourth,  £. 

So.  A  physician  charged  a  patient  83  for  3  visits.    How 
much  did  he  charge  for  one  visit  ? 

3G.  If  I  divide  18  Brazil-nuts  equally  among  3  children, 
how  many  nuts  shall  I  give  to  each  child  ? 

37.  If  a  steam-ship  uses  27  tons  of  coal  in  3  days,  how 
much  docs  she  use  in  one  day  ? 

38.  A  farmer  plowed  12  acres  of  land  in  4  days.    How 
many  acres  did  he  plow  in  one  day  ? 

30.  In  an  orchard,  24  trees  stand  in  4  equal  rows.    How 
many  trees  are  there  in  a  row  ? 

40.  A  lady  used  20  yards  of  lace  in  making  curtains  for 
4  windows.     How  many  yards  did  she  use  for  each 
window  ? 

41.  How  many  hours  must  a  man  work  each  day,  to  do 
30  hours'  work  in  3  days  ? 

42.  If  4  quarts  of  blue-berries  cost  28  cents,  how  much 
will  one  quart  cost  ? 

43.  A  furrier  sold  4  buffalo-robes  for  840.     How  much 
did  he  receive  for  each  robe? 


46  I  I  R  S  T    C  O  U  R  S  L    IN     INTEGERS. 

44*  If  3  tons  of  coal  cost  $24,  how  much  will  1  ton  cost  ? 

\  carman  drew  36  barrels  of  lim  ,nal  loads. 

How  many  barrels  did  he  draw  at  one  load 

In  solving  each  of  the  first  twenty-one  problems  in  this 
Section,  we  found  how  many  times  one  of  two  numl>crs  of  the 
same  kind  is  contained  in  the  other;  and  in  solving  each  of 
the  other  problems,  we  separated  one  of  two  numbers  into  as 
many  equal  parts  as  there  arc  ones  in  the  other. 

n  is  the  process  of  finding  how  ninny  times  one  of 
two  numbers  is  contained  in  the  other ;  or  of  finding  one  of  the 
equal  parts  into  which  a  number  may  be  divided. 
The  Quo fi cut  is  the  result  obtained  by  division, 
The  •/><> -i dcnd  is  the  number  to  be  divided. 

'Divisor  is  the  number  by  which  ;  ^  to  be 

di\i«le  1. 

The  Sign  of  Division,  made  thus,  -*-,  when  placed  be- 
tween two  numbers,  signifies  that  the  number  before  i 
be  divided  by  the  number  after  it.     It  is  read,  "divided  l>y. 
Thus,  85  -i-  7  is  read,  "  85  divided  by  ; 

28,  and  the  divisor  is  4.     What 
quotient  ? 

47.  What  is  the  quotient  of  $40  divided  l.y  4 1 

48.  27  -4-  8  =  how  many  t 

49.  How  many  are  12  -j-  2  ? 
60.   15  -f-  5  =  what  number  ? 

5L  A  man  paid  $25  for  coal,  at  $5  a  ton.     How  many 
tons  did  he  buy  ? 

.".'.   How  many  .Vdollar  bills  must  a  butcher  pay,  fora 

cow  that  costs  him  $40  ? 
55.   85  miles  are  how  many  times  5  miles  t 
64.  A  grocer  sells  raisins,  at  5  pounds  for  a  dollar.   How 

many  dollars  will  he  r  r  45  pounds  ? 


DIVISION.  47 

55.  A  lady  taught  school  50  days,  teaching  5  days  in  a 
week.     How  many  weeks  did  she  teach  ? 

56.  A  carpenter  framed  a  barn  in  12  days.     How  many 
weeks  did  it  take  him  ? 

57.  lie  finished  the  barn  in  24  days  more.    How  many 
weeks  was  he  in  finishing  it  ? 

58.  When  shingle  nails  cost  6  cents  a  pound,  how  many 
pounds  can  be  bought  for  36  cents  ? 

50.  How  many  weeks  arc  there  in  42  working  days  ? 

60.  48  tea-spoons  are  how  many  sets  ? 

61.  Celia  paid  18  cents  for  thread,  at  G  cents  a  spool. 
How  many  spools  did  she  buy  ? 

62.  If  a  farm  hand  can  hoe  5  acres  of  corn  in  5  days, 
how  many  acres  can  he  hoe  in  one  day  ? 

63.  Bertha  picked  18  quarts  of  berries  in  6  hours.   How 
many  quarts  did  she  pick  in  one  hour? 

When  any  number  of  things,  ones,  or  units  is  divided  into  five 
equal  parts,  one  part  is  one  fifth  of  the  number  divided;  and 

When  any  number  of  things,  ones,  or  units  is  divided  into  six 
equal  parts,  one  part  is  one  sixth  of  the  number  divided. 

One  fifth  is  written  £ ;  and  one  sixth,  $. 

64.  How  many  pens  are  ^  of  10  pens  ? 

65.  How  many  pencils  are  |  of  6  pencils  ? 

66.  If  5  baskets  of  peaches  cost  $10,  how  much  will  one 
basket  cost  ? 

67.  A  piece  of  land  containing  20  acres  was  fenced  off 
into  5  equal  fields.    How  many  acres  were  there  in 
each  field  ? 

68.  A  carpenter  gave  30  cents  for  5  lead-pencils.     How 
much  did  he  pay  apiece  for  them? 


48  Finsx  co u RSI:   IN    INTI:GERS. 

69.  One  month  a  teamster  fed  30  bushels  of  oats  to  6 
Imrses.    How  many  oats  did  he  feed  to  one  horse  ? 

70.  A  laborer  bought  a  cow  for  $3G,  and  paid  for  1 

jiial.  monthly  payments.     llo\v  much   I 
pay m- -in  ? 

71.  If  42  pounds  of  bur  from  tin-  milk 
of  6  cows,  in  a  week,  how  many  pounds  can  be  made 
from  tlu-  milk  of  one  cow,  at  the  same  r 

72.  A  joiner  cut  a  strip  of  molding,  25  inches  long,  into 

s.     How  long  was  each  piece  ? 

73.  If  one  :n  do  a  piece  of  work 
how  many  days  can  5  men  do  it  ? 

74-  In  a  ganl -n   are  48  strawberry  plants,  i: 

rows.    How  many  plants  :. 
75.  How  many  days  will  it  take  a  man  to  do  54  hours' 

work,  if  h.   works  G  hours  each  day? 

70.  One  4th  of  July,  Jerome  spent  28  cents  for  fnv- 
crackers,  at  7  cents  a  bunch.  How  many  bunches 
did  he  buy? 

, :.  How  many  bananas  can  be  bought  for  14  cents,  at 
7  cents  apiece  ? 

78.  60  -T-  8  =  how  many  ? 

70.  A  and  B  are  driving  on  the  road,  in  the  sanc- 
tion, ainl  A  is  56  rods  ahead  of  B.     In  how  many 
minutes  will  J5  overtake  A,  if  he  gains  7  rods  in  a 
minute? 

80.  How  many  weeks  will  it  take  a  girl  to  bra' 
palm-leaf  hats,  if  she  braids  9  hats  in  a  week  ? 

SI.  Into  how  many  lots,  of  9  acres  each,  can  27  acres  of 
land  be  divided  ? 

82.  How  many  papers  of  carpet  tacks  can  be  bought  f<»r 
16  cent*  at  8  cents  a  paper? 


DIVISION.  49 

83.  Nathan   paid   9   cents  for  cocoa-nuts,   at   9   cents 
apiece.     How  many  cocoa-nuts  did  he  buy  ? 

SJf.  At  $8  a  ton,  how  many  tons  of  hay  can  be  bought 
for  $32  ?    How  many  tons  for  $64  ? 

85.  30  soldiers  were  detailed  for  duty,  in  squads  of  10. 
Into  how  many  squads  were  they  divided  ? 

86.  How  many  papers  of  needles  can  be  bought  for  48 
cents,  at  8  cents  a  paper  ? 

87.  At  9  cents  apiece,  how  many  pine-apples  can  be 
bought  for  36  cents  ?     How  many  for  54  cents  ? 

88.  How  many  sheets  of  drawing  paper  can  I  buy  for 
40  cents,  at  10  cents  a  sheet  ? 

89.  Ella  paid  60  cents  for  strawberries,  at  10  cents  a 
quart.     How  many  quarts  did  she  buy  ? 

99.  Rosa  bought  some  ribbon,  at  8  cents  a  yard,  and 
paid  72  cents  for  it.    How  many  yards  did  she  buy  ? 

ft  I.  When   filberts   are   9   cents  a  pound,  how   many 
pounds  can  be  bought  for  63  cents  ? 

a.'.  At  $8  a  bushel,  how  many  bushels  of  clover  seed 
can  be  bought  for  880  ? 

93.  David  received  81  cents  for  walnuts,  at  9  cents  a 
quart.     How  many  quarts  did  he  sell  ? 

94.  How  many  bushels  of  charcoal,  at  9  cents  a  bushel, 
can  be  bought  for  90  cents  ? 

95.  How  many  bushels,  at  10  cents  a  bushel  ? 

96.  A  painter  received   $100   for  painting  wagons,  at 
$10  apiece.     How  many  wagons  did  he  paint  ? 

07.  If  7  tons  of  coal  cost  $35,  how  much  will  one  ton 

cost? 
98.  A   grocer   sold   7  bushels   of  cranberries  for  $21. 

How  much  did  he  get  a  bushel  for  them  ? 


•  »<>       IIKST  COURSE  IX  INTEGERS. 

One  of  tetcn  equal  part*  into  whirh  any  number  of  things,  one*, 
or  units  in  '»l,  i#  one  seventh  •'  AT/ 

One  of  eight  equal  part*  in  one  eighth  ; 

One  of  nine  equal  partt  it  one  ninth  ;  and 

One  of 'ten.  equal  parts  i»  one  tenth. 

One  seventh  is  written  )  ;  one  eighth,  \  ;  one  ninth,  |;  and 
one  tenth,  TV 

90.  *  of  14  days  arc  how  many  days  ? 

100.  I  of  8  reams  of  pa]>«  r  aiv  liow  many  reai; 

101.  A   lan.i-T  used  56  rails  in  making  7  lengths  of 

.  many  rails  did  he  use  for  •  ^\\\  \ 

' >n<-  man  can  do  a  certain  piece  of  w 
-.     In  how  many  days  can  7  m«-n  d<>  it  ? 

103.  A  gentleman  paid  $G3  for  7  weeks'  board.     II  \\- 
much  was  that  p 

104.  Ira  sold  7  bunches  of  grapes  for  49  cents, 
much  did  he  get  for  one  hunt 

106.  Edwin  paid  70  cents  for  7  pints  of  pea-nuts.     II   >v 
iniu-h  did  they  cost  a  pint  ? 

106.  A  boot  maker  received  $16  for  making  8  pairs  of 
coarse  boots.  How  much  did  he  receive  for  making 
one  pair? 

107.  In  a  game  of  base-ball  there  were  8  boys  on 
side.     One  side  kept  their  innings  until  tln-y  had 
ha  1  -.'  1  knocks.     How  many  knocks  did  each  boy 
hai 

108.  A  gardener  sold  9  quarts  of  currants  for  45  cents. 
II  >w  much  did  he  get  a  quart  for  them  ? 

!  f  I  give  20  apples  for  10  pears,  how  many  apples 
do  I  give  for  one  pear  ? 

110.  A  carman  received  40  cents  for  drawing  8  K. 
of  flour.     How  much  was  that  per  ban 


DIVISION.  51 

111.  A  crockery  dealer  bought  10  China  tea-sets  for 
$90.    How  much  did  one  set  cost  him  ? 

112.  A  wood  dealer  sold  10   cords  of  wood  for  $50. 
"\Vhat  was  the  price  per  cord  ? 

113.  A  stove  dealer  bought  10  parlor  stoves  for  $80. 
What  was  the  price  of  each  ? 

114.  A  boy  sold  9  quarts  of  cherries  for  72  cents.    How 
much  did  he  get  a  quart  for  them  ? 

115.  If  10  sets  of  silver-plated  forks  cost  $GO,  how  much 
will  one  set  cost  ? 

11G.  A  farmer  gathered  100  bushels  of  apples  from  10 
trees.     How  many  bushels  was  that  to  each  tree  ? 

111.  A  blacksmith  paid  56  cents  for  8  pounds  of  nail- 
rod  iron.     How  much  was  the  iron  per  pound  ? 

118.  A  merchant  paid  72  dollars  for  8  pieces  of  dress 
goods.    How  much  did  they  cost  per  piece  ? 

110.   How  many  times  is  2  contained  in  2  ?   In  4  ?  In  C  ?  In  8  ? 
In  10?    In  12?     In  14?     In  16  ?     In  18?     In  20? 

120.  Divide  by  3,  from  3  in  3  to  8  in  30,  thus :  3  in  3,  once ; 

3  in  6,  2  times ;  3  in  9,  3  times ;  and  so  on. 

121.  Divide  by  4,  from  4  in  4  to  4  in  40 ;  thus :  4  in  4,  once ; 

4  in  8,  2  times  ;  4  in  12,  3  times ;  and  so  on. 

122.  How  much  is  £  of  2 ?    £ot'4?   £of6?  £of8?    £oflO? 
£of!2?    £of!4?     £of!6?    £of!8?     |of20? 

(See  Manual,  page  172.) 

123.  How  much  is  £  of  3?  £ofG?   £of9?  £ofl2?    £  of  15  2 
£of!8?     |  of  21?     £of24?     £of27?     $  of  30  ? 

124.  How  much  is  |  of  4  ?  £  of  8  ?  ±  of  12  ?  £  of  16  ?   £  of  20  ? 
|of24?    £of28?     ±of32?    £  of  36  ?    £of40? 

125.  How  many  times  is  5  contained  in  5  ?     In  10  ?     In  15  ? 
In  20  ?     In  25  ?   In  30  ?    In  35  ?    In  40  ?    In  45  ?    In  50  ? 

126.  Divide  by  6,  from  C  in  6  to  6  in  60 ;  thus :  6  in  G,  once  ; 
6  in  12,  2  times ;  6  in  18,  3  times ;  and  so  on. 


FIRST  corn- 1:    i  \    i  x  r  I 

127.  Divide  by  7,  from  7  in  7  to  7  in  70. 

128.  Find,  successively,  |  of  5,  10,  15,  20,  25,  30. 
and  50. 

1W.   Find,  successively,  \  of  6,  12,  18,  24,  30,  3C. 

and  00. 
ISO.  Find,  successively,  |  of  7,  14,  21,  28,  85,  42,  49, 

and  70. 

I'll.  Divide  by  8,  from  8  in  8  to  8  in  80. 
139.  Divide  by  9,  from  9  in  9  to  9  in  90. 

133.  Divide  by  10,  from  10  in  10  to  10  in  100. 

134.  Find,  successively,  \  of  8,  18,  24,  82,  40,  48,  56,  64,  72, 
and  80. 

135.  Find,  successively.   ;   of  0,  is,  27,  30,  45,  54 
and  90. 

136.  Find,  successively,  -,1*  of  10,  20,  80,  40,  50,  60,  70,  80,  90, 

i  100. 


SECTION  VII. 


1.  KMMA  bought  M  ncils,  at  5  cents  a] 

a  sheet  of  drawing  paper  for  8  cents.    How  much 
money  did  she  pay  out  ? 

2.  A  man  earns  $9  a  week,  and  his  son  $4.     If  the 
fath.-r  v,  reks,  and  the  son  1  wn-k.  how  much 
do  they  earn  ?    Method*,  page  ITS. 

3.  A  farmer  gave  10  barrels  of  apples,  worth  $3  a  bar- 
ivl,  and  $5  in  money,  for  a  suit  of  clothes.     What 
was  the  cost  of  the  cloth 

4.  How  many  days  are  5  times  8  days,  +  9  days  t 

.    Mow  many  hours  are  7  times  7  hours,  -f  10  hours? 

6.  How  many  miles  are  9  times  6  miles,  +  7  miles  ? 

7.  8  times  7  feet,  +  6  feet  are  how  many  feet  ? 

5.  6  timps  10  ynr.N.  :   :i  y:ir«l-  :m>  ln>w  many  yards? 


RE  VIEW     PROBLEMS.  53 

0.  Aaron  sold  4  melons,  at  9  cents  apiece,  and  ex- 
pended all  the  money  but  6  cents  for  a  slate.  How 
much  did  the  slate  cost  him  ?  Methods,  page  175. 

10.  Julius  gave  2  10-cent  pieces  to  pay  for  a  writing- 
book,  and  received  5  cents  in  change.  What  was  the 
cost  of  the  writing-book  ? 

11.  How  many  bushels  arc  4  times  7  bushels,—  9  bushels  ? 
U.   How  many  pecks  arc  3  times  9  pecks,—  5  pecks  ? 

18.   6x7  quarts,—  4  quarts  =  how  many  quarts  ? 

14.  9x5  pints,—  10  pints  =  how  many  pints  ? 

15.  If  C  travels  east  3  miles  an  hour,  and  B  west  5 
miles  an  hour,  how  far  apart  will  they  be  in  6  hours  ? 

(Sec  Manual,  page  173.) 

16.  If  they  both  travel  in  the  same  direction,  how  far 
apart  will  they  be  in  8  hours  ? 

17.  A  grocer  sold  7  pounds  of  starch  to  one  customer, 
and  3  pounds  to  another,  at  9  cents  a  pound.     How 
much  did  he  receive  ? 

18.  If  7  pairs  of  cuffs  can  be  made  from  1  yard  of  linen, 
how  many  pairs  can  be  made  from  two  pieces,  one 
containing  4  yards,  and  the  other  5  yards  ? 

19.  How  many  gallons  are  6  x  3  gallons,  +  4  gallons  ? 

20.  How  many  half-pints  are  10  times  2  half-pints,  +  C  half- 
pints  ? 

21.  A  grocer  having  14  oranges,  sold  all  but  5  of  them, 
at  3  cents  apiece.    How  much  did  he  get  for  those 
he  sold  ? 

2.1.  How  much  will  be  the  cost  of  9  sheep,  at  $3  apiece ; 

and  2,  at  $4  apiece  ? 
23.  A  confectioner  sold  7  ounces  of  candy,  at  6  cents  an 

ounce;  and  2  ounces,  at  5  cents  an  ounce.    How 

much  did  he  receive  ? 


54  FIRST    COURSE    IX     INTEGERS. 

24.  Pauline  practices  on  her  piano  3  hours  every  I 
day,  and  spends  '2  hours  with  her  drawings  i 
in  a  week.  IIow  many  hours  in  a  week  does  she 

>te  to  drawing  and  music  ? 
..  ".    <>  times  7  -H  2  times  5  =  how  many? 

:'.  a  how  many  ? 
times  10  arc  how  many  more  than  4  times  21 

28.  8  times  7,—  0  are  how  many  ? 

29.  4  times  9,  —  5  are  how  many  ? 

.  ".    I  low  many  are  9  times  8,  less  7 1 
.•;/.    How  nr.my  :irv  7  timrs5,leSB  8  t 

..'.'.  If  :i  i:.  i  ditch  in  9  days,  h»»w  : 

diiT  it   in  GDC  day?     Method*,  page  17-.. 

.11  in  7  days,  in  how  many 
days  can  one  man  lay  it  ? 

34*  How  many  men  will  l>e  n-qtiir  the  same 

wall  in  one  day  ? 

of  hay  will  keep  9  sheep   1  nn.nt!.-.     II    ., 
many  months  will  it  keep  one  she 

.    .    How  many  months  will  it  keep  U  sh- 

..   If  :;  ootdl  «\'  wood  cost  $18,  how  much  will  I 

cost?     How  much  will  :>  cords  cost? 
38.  In  how  many  d  L  6  in  n  dig  a  cellar,  that  3 

i  di:;  in  10  d;: 

.  A  mechanic  ran  htiild  a  sidewalk  in  .">  days,  wcrk- 
in-_T  0  hours  a  day.  In  how  many  days  can  he  build 
it.  working  10  hmirs  a  d:: 

40.  If  G3  yards  of  bhi'-  broadrloth  will  make  T  uniforms. 
Imw  many  yards  will  makr  -\  uniforms:' 

41.  4  times  9  are  how  many  times  0  ?    M>  Mhwtef  ;•"?/'    i7.~. 
JS.   8  times  10  are  how  many  times  times  6 1 


HE  VIEW     PROBLEMS.  55 

43.  6  times  4  are  how  many  times  3  ?     How  many  times  2  ? 
How  many  times  8  ?     How  many  times  12  ? 

The  factors  of  12,  in  sets  of  two  each,  are  2  and  6,  or  3  and  4. 

44.  What  are  the  factors  of  14,  in  sets  of  2  each  ?     Of  15  ? 
Of  16  ?     Of  18  ?     (See  Manual,  page  173.) 

A  number  that  can  be  separated  into  factors,  is  a  Composite 
Nwnber. 

45.  Name,  in  sets  of  two  each,  the  factors  of  all  the  composite 
numbers  from  1  to  10.     From  10  to  20. 

46.  Name,  in  sets  of  two,  the  factors  of  the  composite  num- 
bers from  20  to  30,  not  using  any  factor  greater  than  10. 

47.  In  the  same  manner,  name,  in  sets  of  two  each,  the  factors 
of  all  the  composite  numbers  from  30  to  40.     From  40  to 
50.     From  50  to  60. 

48.  Name,  in  sets  of  two,  the  factors  of  the  composite  num- 
bers from  60  to  100,  not  using  any  factor  greater  thao  10. 

49.  54  is  how  many  times  9  ? 

50.  64  is  how  many  times  8  ? 

51.  36  is  how  many  times  4  ?     How  many  times  6  ? 

52.  28  is  4  times  what  number  ? 

53.  45  is  9  times  what  number  ? 

54.  63  is  7  times  what  number  ? 

55.  How  much  is  \  of  2  times  10  ?    Methods,  parjc  173. 

56.  How  much  is  £  of  6  times  6  ? 

57.  How  much  is  ^  of  6  times  5  ? 

58.  How  much  is  £  of  2  times  6  ? 

59.  If  £  ton  of  hay  costs  $7,  how  much  will  a  ton  cost  ? 
GO.  If  |  acre  of  land  is  worth  $10,  how  much  is  1  acre 

worth  ? 

Gl.  If  a  mechanic  can  earn  9  cents  in  t  of  an  hour, 
how  much  can  he  earn  in  an  hour  ? 

o1.?.    Of  what  number  is  1  1  half?   1  third  ?   1  fourth  ?   1  fifth  ? 
?     1  seventh  ?     1  eighth  ?     1  ninth  ?     1  tenth  ? 


56  FIBST   COUBSI:    IN    iMi:.ii:us. 

63.  Of  what  number  is  2  1  half?    1  third  ?    1  fourth  ?   1  fifth  ? 
1  sixth  ?     1  seventh  ?     1  :ith  ? 

64.  Of  what  number  is  3  1  half?    1  third  (    1  fourth  ?    1  fifth  ? 

thl     1  seventh  ?     1  eighth  ?     1  ninth  : 

Of  what  number  is  4  1  half?    1  third  ?   1  fourth  \    1  fifth  ? 

1  sixth?     1  seventh  ?     1  eighth  ?     1  nit  nth.' 

66.   Name,  successively,  the  numbers  of  which  5  is  $,  |,  f  |, 

l»  I,  li  f  ^d  lV     (S«e  Manual,  page  173.) 
C7.  Name,  successively,  the  numbers  of  which  G  is  J,  $,  J,  |, 

ififand^. 
££.   Name,  successively,  the  numbers  of  M  ->i»i»|» 

fcttfcfcndA* 

6P.   Name,  success  numbers  of  which  8  b  J,  J,  J,  |, 


Name,  successively,  the  numbers  of  which  9  is  4,  J,  |,  {, 
|,  f  |,  |,  and  ^. 

A  miller  sold  a  barrel  of  fine  flour  for  $7,  a  kinvl 
of  family  Hour  for  $9,  and  a  barrel  of  XX  flou: 
$11.     What  was  the  average  price?   Method*,  P.  / 

Martin's  standing  in  his  arithmetic  class  on  Mon- 
day was  7;  on  Tuesday,  9  ;  on  Wednesda 

Thursday,    in  ;  and   on    Friday,  s.      What'wa.- 
average  standing  for  k  ? 

73.  A  butcher  bought  2  calves,  at  $7  and  ono 

calf  for  $10.    What  was  their  average  cost  ? 

I  n  4  hours  a  hors  .9  miles,  8  miles, 

and  5  miles.    What  was  his  average  rate  of  spe- 

low  much  is  7  times  \  of 
Mow  much  is  9  times  |  of 

i-»w  much  is  6  times  f  of  63? 

78.  How  much  is  8  times  £  of  28  ? 

79.  How  much  is  5  times  -,V  of  80  ? 

80.  How  much  is  10  times  \  of  81  ?    (See  Manual,  page  173.) 


CHAPTER   II. 


*K|      __:OND  COURSE  IN  INTEGERS.      ]; 

^^-H^^    ^  a 

"**<** 


SECTION    I, 


9.  From  10  and  10  to  100  and  100. 

1.  IF  a  cultivator  costs  $10,  and  a  cart  $30,  what  is  the 
cost  of  both  ? 

2.  A  traveler  has  come  40  miles,  and  he  has  30  miles 
yet  to  go.    What  is  the  length  of  his  journey  ? 

8.  At  what  price  must  an  agent  sell  a  sewing-machine, 
that  cost  him  880,  to  gain  $20? 

4.  A  merchant  bought  a  chest  of  Old  Hyson  tea,  con- 
taining 90  pounds,  and  a  chest  of  Young  Hyson, 
containing  GO  pounds.     How  many  pounds  of  tea 
were  there  in  both  chests  ? 

5.  A  butcher  killed  two  sheep,  one  of  which  weighed 
GO  pounds,  and  the  other  70  pounds.     How  much 
did  both  sheep  weigh  ? 

6.  A  farmer  sows  20  acres  of  land  to  oats,  30  to  wheat, 
and  10  to  corn.     How  many  acres  does  he  sow  ? 

7.  A  farmer  has  30  Saxony,  40  South-Down,  and  50 
merino  sheep.     How  many  sheep  has  he  ? 

5 


58  SECOND    COURS  1. 

8.  I  paid  30  cents  for  a  pound  of  coffee,  and  1-1 
for  a  quart  of  molasses.    How  much  did  1  JK 

both  ?     M,t/,ods,  page  175. 

9.  A  boy  gave  GO  cents  for  a  knife*,  un<l 

box  of  water-colors.    How  many  cents  did  h. 
for  both  ? 

10.  A  grazier  has  70  bead  of  cattle  in  one  pa 

41  head  in  another.     How  many  cattle  has  he  in 
both  past u  i 

11.  A  cotton  manufacturer  sold  40  bales  of  shcr 
and  38  bales  of  shirtings.    How  many  bales  of  i 
kinds  of  goods  did  lie  sell? 

/ .'.  I  n  one  week  a  shoe  dealer  sold  70  cases  of  boot 
56  cases  of  shoes.    How  many  cases  did  lie  s-.-ll ? 

til  dealer  bought  30  pairs  of  gloves,  40  pairs 
18  pairs  of  gauntlets.    How  many 
pairs  of  all  kinds  did  h«-  1 

14.  One  day  a  peddler  sold  a  gold,  hunter-case 

f.T  $100,  an  open-face,  gold  watch   for  $i!U,  and  a 
silver  watch  for  $25.     How  much  did  he  r 

the  three  watch 

15.  A  railroad  company  bought  80  cords  of  wood  at 
one  station.  »;:>  eonls  at  another,  and  4  cords 
third.     How  many  cords  of  wood  did  they  buy  ? 

16.  In  a  village  school  are  24  girls,  and  15  boys.     How 
many  pupils  are  in  that  school? 

:i  cents  for  a  pietuiv.  and  18  cents  for  a 
frame.     How  much  did  both  cost  him  /;.-. 

18.  Harriet  paid  <',:',  .  and  31  cents  for  coffee. 
How  much  did  her  purchases  amount 

19.  A  marble  dealer  paid  $48  for  a  block  of  IP. 

$12  for  freight  on  i:.     What 


SUBTRACTION.  59 

20.  Owen  gave  45  cents  for  a  -pair  of  skates,  and  18 
cents  for  straps.     How  much  did  they  cost  him  ? 

21.  Helen's  furs  cost  $28,  and  Lucy's  cost  $27.    How 
much  did  both  sets  cost ?  ^\ 

£?.  Eva  paid  38  cents  for  lace,  and  25  cents  for  ribbon. 
How  much  did  she  pay  for  both  ? 

23.  In  one  week  a  hotel  keeper  received  $37  from  board- 
ers, and  $54  from  travelers.  What  were  his  receipts 
for  the  week  ?  •  \ 

££•  A  farmer  has  89  sheep,  and  24  lambs.  How  many 
sheep  and  lambs  has  he  ? 

26.  Upon  a  steam-boat  there  are  92  gentlemen,  and  57 
ladies.  How  many  passengers  arc  on  the  boat  ? 

26.  How  many  men  are  96  men  -f  15  men? 

27.  How  many  horses  are  41  horses  and  98  horses  ? 

28.  $34  +  $27  +  $45  =  how  many  dollars  ?      '  £  ,    - 

29.  56  sheep  -f  18  sheep  +  68  sheep  =  how  many  sheep  ?    • 
SO.  What  is  the  sum  of  44,  37,  16,  and  7  ? 


SECTION    II. 

ft  A.  C  T 
10.  From  20  minus  10  to  200  minus  100. 

1.  A  MAN  owing  a  debt  of  $30,  paid  all  but  $10.   How 

much  did  he  pay  ?     Methods,  page  175. 

2.  Jesse  had  100  cents,  but  he  paid  20  cents  for  admit- 
tance to  a  concert.    How  many  cents  had  he  left  ? 

3.  A  fish-monger  sold  CO  pounds  of  steak,  from  a  hali- 
but that  weighed  80  pounds.    How  much  remained 
unsold  ? 


50      SECOND  COURSE  IX  INTEGERS. 

4.  From  a  hogshead  of  West  India  molasses  which 
contained  110  gallons,  70  gallons  have  been  drawn 
out.  How  many  gallons  are  1 

.".  Philip  threw  his  ball  against  a  barn  50  feet  d. 
and  it  rebounded  30  feet     How   far  was  it   then 
from  him  ? 

6.  A  cutler  having  90  knhvs,  .--..Id  -10  of  them.     Ib>\v 
my  had  he  left? 

tinman  having  70  sheets  of  tin,  used  50  sheets  for 
pans,  and  the  rest  f «  ;  IIow  many  f! 

h.'  make  into  pa!. 

8.  A  lady  went  shopping  with  $C3,  and  had  $20  when 
she  return  d.  How  much  ha-!  :it  ? 

'  ~t:>  giufti  irha  I 

rem  _r!it.    How  many  left  : 

JO.  A  farm,  r  liaving  79  fleeces  of  wool,  sold  30  11 
How  many  had  he  left  ? 

11.  A  physician  paid  $87  for  a  horse,  and  $60  less  for  a 
harness.     How  much  did  the  harness  cost  h 

-hipped  96  bottles  of  win-   to  a  eu.-- 
but  only  80  rea< ;  unbroken. 

many  were  brokrii  ? 

book-binder  bought  72  sheets  of  straw-board,  and 
d  60  of  tin-ill.     H<>w  many  had  he  1- 
J4*  A  builder  bought  (HI  barrds  nf  water-lim.-.  and  nsed 
81  barrels.    How  many  barrels  had  lu  : 

irrain  buy.  r  bought  wheat  at  90  cents  a  1>; 
and  sold  it  at  108  cent-.     How  much  did  he  gain  a 
bushel  ? 

16.  Elvira  is   16    years    old,  and   Laura  is  13 
How  old  is  Lai;. 


SUBTRACTION.  61 

17.  From  a  piece  of  sheeting  containing  39  yards,  a 
merchant  sold  15  yards.    How  many  yards  were  left 

in  the  piece  ?      Methods,  page  176. 

18.  A  shoe  dealer  bought  48  "boxes  of  blacking,  and  sold 
25  boxes.     How  many  boxes  had  he  left  ? 

10.  Luke  and  Ezra  ran  a  race.  Luke  ran  G9  rods,  while 
Ezra  ran  58.  How  many  rods  did  Luke  beat  Ezra  ? 

20.  A  manufacturer  made  53  hay  rakes  in  a  week,  and 
sold  44  of  them.     How  many  had  he  left  ? 

21.  A  farmer  earned  72  bundles  of  straw  to  the  city, 
and  sold  56  bundles  in  the  forenoon.     How  many 
had  he  to  sell  in  the  afternoon  ? 

£;?.  A  coal  dealer  bought  83  tons  of  stove  coal,  and  57 
tons  of  chestnut  coal.  How  much  more  of  the  stove 
than  of  the  chestnut  coal  did  he  buy  ? 

,?J.  A  grocer  bought  one  cheese  weighing  91  pounds, 
and  another  weighing  26  pounds  less.  How  much 
did  the  second  cheese  weigh  ? 

24.  Upon  a  note  of  875,  $47  have  been  paid.     How 
much  is  yet  due  ? 

25.  In  my  farm  there  are  84  acres,  19  acres  of  which 
are  woodland.     How  much  cleared  land  have  I  ? 

26.  In  the  town  of  Essex  there  are  76  square  miles,  and 
in  Franklin  39  square  miles  less.   How  many  square 
miles  are  there  in  Franklin  ? 

27.  97  —  49  =  how  many  ? 

28.  103  pigeons  —  69  pigeons  =  how  many  pigeons  ? 
SO.   Ill  swallows  are  how  many  more  than  28  swallows  ? 
SO.   108  robins  —  99  robins  are  how  many  robins  ? 

31.   50  cents  are  how  many  less  than  100  cents  ? 


62  SECOND     COURSE     IX     IXTi:«;i:RS 

SECTION  III, 


11.   From  10  times  10  to  10  times  100. 

1.  Ax  $20  an  acre,  how  much  will  3  acres  of  land  cost? 
..'.  A  m-rcliant   s.dd   4  shawls,  at  $30  Bpieoe,      How 

much  did  he  receive  for  them  ?    M 
»?.  How  many  yards  in  5  pieces  of  brown  linen 

piece  containing  40  yards? 

4.  A  wagon  maker  sold  3  light  wagons,  at  $90  a; 
How  much  did  he  get  for  them? 

5.  How  much  will  50  pounds  of  sugar  cost,  at  10 
a  pound  ? 

'     II  o\\-  murh  must  I  pay  for  40  boxes  of  table  salt.  :it 

9  cents  a  box  ? 
;.   I  low  many  yard-:  in  '?  pieces  of  carpel 

containing  70  yards? 
8.  A  man  tra\.  -1.  -d  7  miles  an  hour  for  GO  hour-.    II     . 

far  did  lie  tnr 
0.  How  murh  will  40  silk  vesta  cost,  at  $G  ; 

10.  How  many  acres  of  land  in  8  Government  lots,  of 
80  acres  each  ? 

11.  How  much  will  ;>  pounds  of  l>utt«-r  cost,  at  23  cents 

a  pound  ?      Method*,  pag*  176. 

J  :.  How  many  yards  an-  there  in  4  pieces  of  oil-cloth, 
each  piece  containing  42  yards  ? 

13.  If  a  boy  emu  :>l  c'-nts  a  day,  how  much  can  h- 
earn  in  5  days  ? 

14.  A  cooper  made  '.»  1-anvls  a  day.  f.ir  "t\  days.     H..-.V 
many  barrels  did  he  mak 

15.  At  $35  Bpieoe,  how  much  will  3  cutters  cost? 


MULTIPLICATION.  G3 

16.  How  much  must  be  paid  for  2  barrels  of  pork,  at 
$26  a  barrel  ? 

17.  How  much  must  be  paid  for  4  bales  of  hops,  at  $44 

a  bale  ?      Methods,  page  176. 

18.  A  fruit  dealer  bought  28   cocoa-nuts,  at  8  cents 
apiece.    How  much  did  they  cost  him  ? 

19.  How  much  must  be  paid  for  bottoming  6  cane-seat 
chairs,  at  45  cents  a  piece  ? 

20.  In  a  barrel  of  K  Y.  State  salt  are  5  bushels,  of  56 
pounds  each.     How  many  pounds  are  in  a  barrel  ? 

21.  How  far  will  a  railroad  train  run  in  9  hours,  run- 
ning 28  miles  an  hour  ? 

22.  A  field  of  10  acres  of  barley  yielded  36  bushels  to 
the  acre.    What  was  the  total  yield  ?  • 

23.  At  75  cents  apiece,  how  much  will  6  school  readers 
cost? 

24.  If  I  pay  6  cents  for  the  use  of  1  dollar  for  a  year, 
how  much  must  I  pay  for  the  use  of  37  dollars  ? 

2o.  How  much  will  84  pairs  of  boots  cost,  at  $5  a  pair  ? 

26.  How  much  will  69  yards  of  cassimere  cost,  at  $2  a 
yard? 

27.  What  will  be  the  railroad  fare  from  A  to  B,  98 
miles,  at  3  cents  a  mile  ? 

28.  A  paper  maker  sold  93  reams  of  book  paper,  at  $7  a 
ream.     How  much  did  it  come  to  ? 

20.  A  freight-train  of  10  cars  is  loaded  with  flour,  each 
car  carrying  86  barrels.  How  many  barrels  are  on 
the  train  ? 

30.  How  much  will  4  cows  cost,  at  $79  apiece  ? 

31.  How  much  will  8  sewing-machines  cost,  at  $56  each  ? 


64     SECOND  COURSE  IX  INTEGERS. 

•; .'.  I  low  much  will  7  acres  of  land  cost,  at  $65  an  acre  ? 
S3.  How  much  will  47  tons  of  hay  cost,  at  $10  a  ton  ? 

strain-boat  plys  between  two  places  that 
mik.s  apart.     How  many  miles  does  she  make  in  8 
trips? 
S5.  9  times  81  are  how  many  ? 

36.  4  times  67  are  how  many  ? 

37.  5  times  84  are  how  many  I 


38.  7  x  27  =  how  many  ? 

39.  6  x  83  =  how  many  ? 


40.  8  x  95  =  how  many  ? 

41.  88  x  8  =  how  many  I 


SECTION    IV. 


1  2.  Prom  2  in  20  to  10  in  1000. 

/.  A    i  A  KM  hand  received  $60  for  3  months'  ^ 
How  much  were  his  monthly  wages  ? 

..   A   milliner  sold  4  yards  of  ribbon  for  80  > 
What  was  tin-  price  per  yard?    Met  hods,  JMW  /;* 

3.  A  tea<-h<  T  paid  360  cents  for  9  dozen  lead  p 
How  much  did  they  cost  him  a  do; 

4.  If  a  factory  pirl  can  weave  180  yards  of  cloth  in  0 
days,  how  much  can  she  weave  in  a  day? 

dairy-man  sold  '.'  cheeses,  the  total  weight  of 
which  was  630  pounds.  What  was  their  average 
weight  ? 

6.  A  milkman  bought  8  cows  for  $320.     TVha 
tlvir  average  cost? 

7.  5  persons  earned  $250  in  a  month.    What  were  their 
average  monthly  earning 


DIVISION.  Go 

S.  A  butcher  killed  8  sheep,  the  aggregate  weight  of 
which  was  720  pounds.  What  was  their  average 
weight  ? 

9.  At  what  price  per  light  will  8  lights  of  French 
plate-glass  cost  $400  ? 

10.  How  many  barrels  of  lime  can  be  bought  for  $153, 
at  $3  a  barrel  ? 

11.  A  man  threshed  48  bushels  of  beans  in  3  days.    How 
many  bushels  did  he  average  per  day  ?    Methods,  170. 

/?.  If  6  boys  pick  up  96  bushels  of  apples  in  a  day, 
what  is  the  average  number  of  bushels  to  a  boy  ? 

13.  Olivia  expended  75  'cents  for  grapes,  at  5  cents  a 
bunch.  How  many  bunches  did  she  buy  ? 

14-  How  many  suits  of  clothes  can  be  made  from  91 
yards  of  cloth,  allowing  7  yards  to  a  suit  ? 

l~>.  How  many  weeks  will  108  loaves  of  bread  last  a 
family,  that  use  9  loaves  a  week  ?  Methods,  page  170. 

16.  A  lady  teacher  received  $175  for  7  months'  services. 
How  much  did  she  receive  per  month  ? 

17.  A  farm  of  415  acres  is  to  be  divided  equally  among 
5  heirs.    How  many  acres  will  each  heir  receive  ? 

18.  A  crockery  dealer  sold  144  plates,  in  sets  of  G  plates. 
How  many  sets  did  he  sell  ? 

19.  A  lawyer  paid  $110  for  5  months'  board.     How 
much  did  he  pay  per  month  ? 

20.  A  farmer  received  $301   for  wood,  at  $7  a  cord. 
How  many  cords  did  he  sell  ? 

21.  In  making  a  book  of  224  pages,  7  sheets  of  paper  are 
us,ed.    How  many  pages  of  the  book  does  each  sheet 
of  paper  make  ? 

6 


nr>  u.Ni)    CO  r  i:  B  ;:    i  N 

..'.'.  How  many  hours  will  it  take  a  steam-boar  t«>  run 
280  miles,  running  8  miles  an  hour? 

•'  C48  chestnuts  be  di\id< -d  equally  among  1' 
how  many  will  each  hoy  t 

railroad   train   ran   ll»s  miles  in  G  hours.     AVhat 
tnoe  did  it  run  per  hour? 

put   up  238  gallons  of  cider  in   7  casks. 
How  much  did  he  put  into  each  cask? 

ni <T< 'hunt's  store  expenses  are  $10  a  day.    In  how 
many  days  will  1  .ses  amount  to  $780? 

27.  During  a  heavy  rain  storm,  that  will  hold 

432  barn -Is  of  into,  was  iill.-d  in  s  hours.     How 
much  wat.-r  ran  into  the  ci>: 

29.  A  a  house  and  lot  for  $8-1 

:•  ii   in   7  r.jual  payments.     ll»w  mu<-!. 
each  p.: 

.   I  low  many  pairs  of  boots,  at  $G  a  pair,  can  be  bought 

SO.  If  7   pounds  of  crushfil  --ost  119  cents,  how 

much  will  1  pound  cost  ? 

\t  $10  a  barrel,  how  many  barrels  of  fish   can   he 
bought  for  $750? 

•  •.'.   How  many   cist«  rn    juimps,   at   $8  ;  MI    he 

bought  for  $448  ? 
S3.  If  7  coal  stoves  cost  $308,  what  is  ih.  price  of  1  ? 

34*  At  how    much  apiece  will   G  lumber  wagons  cost 
$588? 

.   At   what  price  per  acre  will  10  acres  of  land  cost 
$910? 


REVIEW     PROBLEMS. 


67 


1.  OXE  winter,  a  farmer  fed  5  tons  of  hay  to  his  horses, 
G  tons  to  his  sheep,  and  14  tons  to  his  cows.    How 
much  hay  did  it  Jake  to  winter  his  live  stock  ? 

2.  How  many  feet  have  all  the  quadrupeds  in  this 
picture  ? 

3.  How  many  pounds  of  wool  are  there  in  11  fleeces, 
that  average  5  pounds  each  ? 

4*  Anson  bought  7  doves,  paying  18  cents  apiece  for 
them.  How  much  did  they  cost  him  ? 

5.  How  much  would  the  teeth  for  a  24-tooth  harrow 
cost,  at  9  cents  each  ? 

G.  A  farmer  milks  9  cows,  and  obtains  135  quarts  of 
milk  daily.  What  is  the  average  number  of  quarts 
to  a  cow  ? 


C8          B  BOO  N  i>    00  r  B8  i:    i  N     i  N  r  BG  i:  B 

7.  If  1  horse  cats  r.*  quart-  of  oat.-  in  a  day,  how  many 
quarts  will  2  horses  cat  in  the  month  of  April  ? 


8.  How  many  per  being  8  quarts  in  a  p« 

''.  II«.\v  many  bushels,  there  being  i 

10.  A  village  school-luuis"  ha-  two  rdoms,  one  of  whic-h 
contains  seats  for  50  pupils,  and  th.  ,-tlu  r,  seats  for 
GO.  How  many  pupils  can  be  seated  in  Loth  KM 

.vsboy  distributes  49  morning  papers,  n: 

iiini:   papers.      H'-w    manj    i  apcrs  doc.- 
tribute  each  day? 

12.  A  draler  I- 

bushels  of  sour  ones.  nyappl- 

^rraph  operator  sent  one  dispatch  of  84  v 

and  another  «»f  o;  words.     How  many  words  ! 
tlu  n-  in  the  two  dispatches? 

14.  Mattlicw  uti«  nd  d  Bobo 

i   7<)  days  in  th«-  winter.     How  many  da;. 

atu-ml  srhonl  in  the  \ 
16.  I  j>aid  a  carpenter  $72  for  building  a  :d  th<- 

lumber  cost  me  $35.     What  was  the  cost  of  th- 

.    V  florist  has  GO  varieties  of  roses,  30  varieties  of 

dahlias,  and  17  Tl  ;m-.      11.  >w  B 

Htfi  kinds  of  flowers  1 

from  the  schnnl-lious.-.  and  walk  east  90 
rods,  and  th  n  w»st  50  rods,  how  far  will  you  be 
from  the  school-house  ? 

18.  At  a  found  ns  of  iron  :uary, 

and  27  ton  ruary.      How   many  tons 

Iran  us.-d  in  1-Vhruar 


REVIEW     PROBLEMS.  69 

10.  Mark  dug  62  bushels  of  potatoes  in  two  days,  dig- 
ging 35  bushels  the  first  day.  How  many  bushels 
more  did  he  dig  the  first  day  than  the  second  ? 

20.  At  $90  a  thousand,  how  much  will  9  thousand  hop- 
poles  cost  ? 

21.  A  surveyor  received  8174  for  his  services,  at  $6  a  day. 
How  many  days  was  he  employed  ? 

At  8  cents  apiece,  how  much  will  48  cocoa-nuts  cost  ? 

2J.  How  many  lengths,  each  9  feet  long,  are  there  in  a 
post-and-rail  fence  783  feet  long  ? 

24.  If  A  can  build  8  rods  of  wall  while  B  builds  5  rods, 
how  many  rods  can  he  build  while  B  builds  35  rods? 

2o.  A  person  bought  3  books,  giving  for  the  first  a 
25-cent  currency  note,  and  receiving  back  10  cents; 
for  the  second  he  gave  20  cents  more  than  the  first 
cost  him,  and  received  back  5  cents ;  the  third  book 
cost  him  as  much  as  the  other  two,  and  he  sold  it 
for  50  cents.  How  much  did  he  gain  on  the  third 
book? 

Philip  lives  40  rods  from  the  school-house,  Edwin 
50  rods  further  away,  and  Arthur  60  rods  further 
than  Edwin.  How  far  does  each  have  to  walk  in 
coming  to  school  ? 

In  building  a  school-house,  a  mason  worked  46  days, 
a  carpenter  64  days,  and  a  painter  18  days.  How 
many  days  did  they  all  work  upon  it  ? 

A  steam-ship  sailed  from  New  York  for  Liverpool 
with  72  first-class,  45  second-class,  and  16  steerage 
passengers.     How  many  passengers  did  she  carry  ? 
?-9.  A  man  owing  $86,  paid  $49  one  day,  and  $18  tho 
next  day.     How  much  did  he  then  owe  ? 


70          SECOND    COUB81    i  .V    i  N  T  r.  i,  i:  us. 

30.  A  map  agent  took  53  subscriptions  in  Januu 

in  1-Vbruary.  47  in  March,  and  :)'.»   in  April.      . 
many  <>rd<T>.  did  In-  take  in  the  four  months? 

->'/.  A  wood  dealer  sold  to  three  persons,  I'.1 

cords,  and  36  cords  of  wood,  and  had  29  cords 
IIn\v  many  cords  had  rst? 

....   I'lMin  a  kiln  of  100  thousand  brick.  31 

\\vn-  sold   to  one  build*  r,  '•   thousand  to  an- 

other.    How  many  brick  In? 

105  cents,  but  he  has 

Edmnn  .ts  to  John,  19  cents  t  .  and 

I'1.  0  nti  1"  M*  1\  in.      II  m  many  cent.- 

•haul    has   M   yards  of  cl..ih   in   f;. 
ii   contains  29  yards,  and  an 
B   '.v  many  yards  m  ;hird 

piece? 

I>cr  paid  $98   for  a  hore< 

$15   for  hi.-  1I«    r«ivi\vd  $3C  for  his  use, 

and  sold  him  lor  $80.    Did  h 
mr. 

.    \   mannfactun  r   mad'-    ','•'>    pain   «-f 

weeks  sold  54  pairs.    How  many  pairs  had  IK  1 

>r  a  sled,  and  50  cents  for  a 

knifv*.  and  gave  thorn  both  f«>r  a  pair  of  skates  worth 
100  cents.    Did  he  gain  or 

88.  I  owe  $120;  $•:  $36  to  B,  $41  to  C.  and  the 

balance  to  D.     Ho\v  niu-.-:  D? 

39.  Oscar  had  40  cents,  and  (Ian  nee  60.     O^r 

as  many  cents  as  Claivn<  .  and  he  then  had 

.    II-.v.-  many  c^nls  did  ('!. 


REVIEW     PROBLEMS.  71 

40.  A  bought  a  watch  for  $65,  and  offered  to  sell  it  for 
$20  more  than  cost,  but  finally  sold  it  for  $16  less 
than  his  asking  price.    At  what  price  did  he  sell  it? 

41.  If  I  go  east  57  miles,  then  west  24  miles,  then  east 
17  miles,  and  then  west  32  miles,  will  ;I  be  east  or 
west  from  the  place  of  starting,  and  how  far? 

42.  From  a  roll  of  carpeting  containing  120  yards,  three 
carpets  of  28  yards,  36  yards,  and  44  yards  were  cut. 
How  many  yards  were  left  in  the  roll  ? 

43.  If  I  deposit  $64  and  $70  in  a  bank,  and  draw  out 
$48,  $36,  and  $25,  how  much  will  I  have  left  in  the 
bank? 

44-  The  railroad  distance  between  Syracuse  and  Roch- 
ester is  81  miles.  If  one  man  leaves  Syracuse,  and 
travels  toward  Rochester  5  miles  an  hour,  and  an- 
other leaves  Rochester,  and  travels  4  miles  an  hour 
toward  Syracuse,  how  far  will  they  be  apart  in  1 
hour  ? 

4~>.  How  far  will  each  have  traveled  in  5  hours  ? 

46.  How  far  will  they  be  apart  in  7  hours  ? 

47.  In  how  many  hours  will  they  meet  ? 

48.  When  they  meet,  how  far  will  each  have  traveled  ? 

49.  How  far  will  the  Rochester  man  go,  while  the  Syra- 
cuse man  is  going  45  miles  ? 

GO.  Mabel  bought  10  yards  of  calico,  at  13  cents  a  yard, 

and  8  yards  of  ribbon,  at  20  cents  a  yard.    How 

much  did  her  purchases  amount  to  ? 
51.  A  drover  bought  25  sheep,  at  $2  apiece ;  34,  at  $3 

apiece  ;  and  18,  at  $4  apiece.    How  many  sheep  did 

he  buy  ? 
5&  How  much  did  they  cost  him  ? 


72  SET  o.\  I)     COURSE     IN*     INTEGERS. 

53.  What  is  the  sum  of  10  times  7,  and  3  times  9  ? 

54.  What  is  the  sum  of  0  x  8  and  5x7? 
What  is  the  sum  of  4  x  7  and  8x9? 

is  the  different  i  9  x  6  and  7x7? 

57.  What  is  the  difference  between  10x6  and  0x8? 

58.  What  is  the  different  i  8  x  7  and  5x9? 

1  Im.-hrl  of  wheat  is  worth  08  much  a> 
of  corn,  and  1  bushel  of  corn  as  much  as  v!  l-u-ln-N 
of  oats,  how  many  bushels  of  oats  ; 
much  as  76  bushels  of  wh 
GO.  A  merchant  bought  5  pieces  of  cam' 

containing  41  yards,  at  10  cents  a  }urd.    I  low  much 
did  it  cost  nim? 

'   '.    How  nv.ny  quiivs  of  j,;  .  .jiiire,  can 

be  bought  i  li  of  doth,  at  30  cents  a  yar 

\  boy  exchanged  3  dozen  of  eggs,  at  33 
doz«-n.  for  4  pounds  of  raisins.    What  was  the  price 

of  tip-  rai-'.is? 

OS.  In  how  many  months  will  8  horses  eat  as  much  as 
10  hors'.s  will  .  at  in  12  months? 

how  man"  days  can  7  men  earn  as  much  as  G 

'  •.  How  mud    grass  seed,  at  $4  a  bushel,  will  pay  for 
invls  of  apples,  at  $3  a  bar 

.   IIo\\    many  noes,  at  80  cents  each,  can  be  bought 

for  10  brooms,  a  b  each  ? 

1  ;.   A  man  has  a  job  of  work  that  lie  can  do   i: 

days.     If  he  employs  5  men  to  assist  him,  in  how 
many  days  will  they  do  i 

(>^\  If  8  men  can  lay  a  mile  of  railroad  track  in  1". 
in  how  many  days  can  12  men  lay 


REVIEW     PROBLEMS.  73 

60.  If  5  yards  of  calico  cost  80  cents,  how  much  will  9 
yards  cost  ? 

70.  If  a  workman  earns  $72  in  8  weeks,  how  much  can 
he  earn  in  24  weeks  ? 

71.  If  a  ship  sails  42  miles  in  7  hours,  how  far  will  she 
sail  in  20  hours  ? 

?~7.  How  many  peaches,  at  the  rate  of  4  for  8  cents, 
can  you  buy  for  22  cents  ? 

73.  A  boy  sold  16  bunches  of  grapes,  at  the  rate  of  3 
bunches  for  15  cents.  How  much  did  he  get  for 
them  ? 

74'  A  farmcr  s°ld  8  barrels  of  apples  at  $4  a  barrel,  and 
enough  more  at  $3  a  barrel,  to  realize  $101.  How 
many  barrels  did  he  sell  at  the  second  price  ? 

75.  One  Fourth  of  July,  Orrin  had  83  cents.   He  bought 
4  bunches  of  fire-crackers,  at  12  cents  a  bunch,  and 
spent  the  rest  of  his  money  for  pea-nuts,  at  7  cents 
a  cup.    How  many  cups  of  pea-nuts  did  he  buy  ? 

76.  A  fruit  dealer  bought  24  baskets  of  peaches,  at  $2  a 
basket,  and  sold  them  all  for  $60.     How  much  was 
his  gain  ? 

77.  A  furniture  dealer  bought  8  wash-stands  for  $40, 
and  sold  thenrat  $6  apiece.   How  much  did  he  gain? 

7S.  A  drover  bought  75  sheep  for  $225,  and  sold  them 
at  $4  apiece.  How  much  did  he  gain  ? 

70.  A  mechanic  worked  for  a  grocer  17  days,  at  $3  a 
day,  and  received  in  pay  $19  in  money,  and  the 
balance  in  groceries.  How  many  dollars'  worth  of 
groceries  did  he  get  ? 

80.  If  the  wages  of  3  men  for  6  days  arc  $36,  what  are 
the  wages  of  4  men  for  8  days  ? 


U  SECOND     COURSE     IX     INTEGERS. 

81.  If  4  men  build  40  rods  of  wall  in  5  days,  how  many 
rods  will  10  men  build  in  G  da; 

82.  8  men,  in  0  days,  made  1  11  pairs  of  shoes.    At  the 
same  rate,  how  many  pairs  will  9  men  mak«- 
days? 

in  1  da\  - 
many  vests  can  1C  girN  make  in  9  days? 

84*  A  dairy -man  who  had  20  cows,  made  900  pounds  of 
rliLvso  iii  15  days.     At   th--  .sun  -w  many 

pounds  of  cheese  can  be  made  in  11  days,  from  the 
milk  of  13  cows? 

85.  10  times  £  of  24  are  bow  many  f 

86.  4  ;  :r>  :ir<  how  many  ? 

•  i  of  48  arc  how  many? 

88.  7  times  ^  of  60  arc  how  many  f 

89.  8  times  J  of  72  arc  how  many  ? 

90.  G  times  }  of  95  arc  how  many  t 

ues  I  of  108  arc  how  many? 
OS.  3  times  ^  of  1 76  arc  how  many  ? 

many  arc  4  times  J  of  10  times  8  f 
I  low  many  arc  6  times  J  of  5  times  9? 
1  low  many  are  5  times  |  of  6  times  12  ? 
I  low  many  iiro  8  times  \  of  9  times  4  ? 

in:iiiy  arc-  7  times  |  of  6  times  Ki  ? 
How  many  arc  9  times  \  of  8  times  7 1 
1)  is  |  of  what  number? 
100.  8  is  \  of  what  mini! 
I.1)  is^  of  what  mini1 

102.  \  of  104  is  |  of  what  nun 

103.  \  of  215  is  \  of  what  mm. 

104.  I  !  of  %\h:i;  I 


y 


CHAPTER  III. 
UNITED  STATES  MONEY, 

SECTION  I. 


VC  TZOJYS. 


77nited  States  Money,  or  Fed- 
eral Money,  consists  of  dollars, 
cents,  and  mills. 

10  mills  are  1  cent. 
100  cents  are  1  dollar. 

1  dollar  is  100  cents. 
1  cent     is    10  mills. 
10  dollars  are  sometimes  called  an  Eagle, 
and  10  cents  a  Dime. 


jm 

K&& 


76 


UNITED    STATES     M  0  .\ 


UNITED   STATES  COIN  TABLE. 


METALS.                KAVXS  OF  COIXS. 

TAI.CRS.     VCTALS. 

5n.  dollar  piece. 

$50.00                   | 

Double  eagle, 

20.00 

Gold,      . 

Btgte, 

Half-eagle, 

10.00   c 

5.0u 

8-dollar  ]> 

3.00 

Quarter-eagle, 

[Del 

1.00                 ( 

(  2-cent  i 
Copper,  j( 

!<el.  • 

.01 

HAVES  OF  COIXS.   VALtTSS. 

f  Dollar.  $1.00 

Half-dollar,         .50 
Quarter-dollar,  .25 


Dime, 
Half-dime. 
3-ecnt  ; 

piece, 


.10 
.03 

.05 
.03 
.01 


If  v  dollar  into  10  equal  parts,  each  of  the  parts 

is  1  tentkof  the  dollar,  and  i-  r  '  ;  2  «• I'  the  part*  are 

x  of  a  doi:  met;  8  parts  are  3  f*v«tf«of  a  dollar. 

or  8  dimes,  and  so  on. 

Dividing  each  of  the  tenths  of  a  dollar,  or  each  din: 
10  equal  parts,  v  dolUrio  times  10.  ..r  loo 

f  these  parts  is  1  hwdrcdth  of  a  dollar, 

l)i\idinur  each  of  the  h  of  a  dol'... 

into  1"  •'.  '•  have  in  the  whole  dollar  I'- 

ll <>f  these  parts  is  1  thoiuaiulth  of  a 
dollar,  and  is  called  1  /  ./"7.     Hence, 

1  tenth  of  1  dollar  is  1  dime,  which  is  written  $.1  or  $.10. 

.th  of  1   dime,  or  1  hundredth  of  a  dollar, 
whieh  is  written  $.01. 

:,th  of  1  cent,  or  1  thousandth  of  a  dollar,  is  1  mill, 
v.liir1.  D  s.nni. 

When  the  dollar  mark  ($)  is  used  in  w riling  any  sum  of 
money,  the  D.\'i'm>il  Pmnt  —  which  is  a  period  or  point  (.)  — 
mu-t  always  be  i  >re  the  cent-.  Thus.  $17.42  ;  $.37. 

From  the  preceding  illustrations  we  see,  that  1  tenth  of  a  1 
is  1  tenth,  and  is  written  .1  ;   1  tenth  of  .1  i-  1 
i-*  written  .01  ;  and  1  tenth  of  .01  is  1  thousandth,  and  i 
ten  .001.     That  ia 


NOTATION    AND    REDUCTIONS.  77 

The  first  place  at  the  right  of  the  decimal  point  is  the  place 
of  tenths,  the  second  place  is  the  place  of  hundredths,  and 
the  third  place  is  the  place  of  thousandths. 

The  first  two  figures  at  the  right  of  the  decimal  point  ex- 
press cents,  and  the  third  figure  expresses  mills.  Thus, 

$.03  expresses  3  cents. 

$.87  "  87  cents. 

$7.03  "         7  dollars  8  cents. 

$3.54  "         3  dollars  54  cents. 

$.007  "         7  mills. 

$.092  "'         9  cents  2  mills. 

$.625  "  G2  cents  5  mills. 

$14.706  "  14  dollars  70  cents  6  mills. 

1.  How  many  mills  are  there  in  4  cents  ? 

2.  How  many  mills  in  10  cents? 

3.  How  many  mills  are  a  half-cent  ? 

4.  5  dimes  are  hpw  many  cents  ? 

5.  3  half-dimes  are  how  many  cents  ? 
C.  How  many  doflars  are  6  eagles  ? 

7.  3  dollars  are  how  many  cents  ? 

8.  10  dollars  are  how  many  cents? 

9.  5  half-dollars  arc  how  many  cents  ? 

10.  Agnes  has  3  dimes  and  a  half-dime.     How  many 
cents  has  she  ? 

11.  Janet  gave  a  half-dollar,  2  dimes,  and,  a  half-dime 
for  a  grammar.     How  many  cents  did  it  cost? 

12.  How  many  dollars  arc  5  eagles  and  a  half-eagle  ? 

13.  How  many  dollars  are  a  double  eagle  and  8  eagles? 

14.  A  man  was  paid  a  50-dollar  piece  for  making  cigars, 
at  a  cent  apiece.     How  many  cigars  did  he  make  ? 

15.  How  many  cents  are  an  eagle  and  a  dollar  worth  ? 

16.  30  mills  are  how  many  cents  ? 

17.  87  mills  are  how  many  cents  and  mills?  Methods,  p.  no. 

18.  100  mills  are  how  many  cents  ? 


78  UNITED    STATES    M01JEY. 

10.  45  mills  are  how  many  rents  ? 

20.  60  cents  are  how  many  dimes  ? 

x'7.    How  many  dimes  and  cents  are  36  cents  ? 

££.   How  many  eagles  are  40  dollars  f 

£J.   How  many  eagles  and  dollars  are  96  dollars  ? 

24.  How  many  picture  books,  at  a  dime  .in  l»o 

bought  for  50  cents? 
~  7.  If  1  ton  of  plaster  costs  a  ha'  ;ow  main 

can  be  bought  for  $70  ? 
26.  A  merchant  exchanged  $120  for  its  value  in  gold 

eagles.    How  in  -  did  In-  r 

i  a  dime  apiece,  how  many  spools  of  thread  can  In- 
bought  for  80  cents? 
tS.  500  cents  are  how  many  dollars  ? 

000  cents  are  how  m  many  eagles  ? 

SO.  How  many  pairs  of  slippers,  at  $1  a  pair,  can  1  Imy 

for  GOO  cents  ? 
.//.   I I«»w  man;.  s,  at  $1  a  -an  !•«.• 

bought  for  900  cents? 

A?.  How  many  cents  are  5  dollars  and  60  cents  ? 
S3.  How  many  cents  are  8  dollars  and  34  cents  f 
Af.  How  many  cents  are  15  dollars  and  0  cei 
SJ.  A  stationer  received  7  dollars  58  cents  for 

cils,  at  1  cent  apii-cf.   How  many  pencils  did  h< 
36.  A  boy  who  prddK-d  apples  at  1  <  >ok  in 

5  dollars  4  cents  in  one  week.     How  many  ni 

did  he  soil? 
. .   How  many  sheets  of  paper,  at  1  cent  a  she.  t.  can  l.-j 

bought  for  10  dollars  7.~>  oenta  ? 
S8.   225  cents  arc  how  many  dollars  and  cents  ? 
£9.    .".  ,:iny  dollars  and  cents? 

40.  How  many  pocket-knives  can  I  Imy  with  \ 

at  $1  apiece,  and  how  many  cents  will  1  ha- 


COMPUTATIONS.  79 

SECTION  II. 

T&TA  TIOJVS. 

1.  NEWTOX  paid  1  dollar  25  cents  for  a  pair  of  birds, 
and  1  dollar  50  cents  for  a  cage.    How  much  did  he 
pay  out  ? 

2.  A  gardener  gave  1  dollar  50  cents  for  a  spade;  88 
cents  for  a  hoe,  and  1  dollar  25  cents  for  a  rake. 
How  much  did  he  give  for  all  ?    Methods,  page  176. 

{/S.  I  paid  $3.50  for  a  coat,  $1.75  for  a  hat,  and  $5.50  for 
a  pair  of  shoes.    How  much  did  they  all  cost  me  ? 

4.  Rufus  gave  $.80  for  a  reader,  $1.40  for  an  arith- 
metic and  slate,  and  $2.25  for  a  geography.    How 
much  did  his  school  books  cost  him  ? 

5.  How  much  will  be  the  cost  of  a  pair  of  scissors  at  45 
cents,  a  penknife  at  81  cents,  a  work  basket  at  94 
cents,  and  a  thimble  at  50  cents  ? 

6.  I  paid  19  dollars  67  cents  railroad  fare,  7  dollars  11 
cents  hotel  bills,  and  3  dollars  GO  cents  for  horse 
hire.    How  much  did  my  journey  cost  me  ? 

7.  Calvin  having  5  dollars  84  cents,  bought  a  ball  and 
bat  for  1  dollar  56  cents.    How  much  money  had  he 

left  ?     Methods,  page  176. 

8.  Edith  took  1  dollar  25  cents,  with  which  to  buy 
some  silk  for  an  apron ;  but  it  cost  only  95  cents. 
How  much  money  did  she  bring  home  ? 

9.  I  owe  7  dollars  48  cents,  and  I  have  5  dollars  75 
cents.     If  I  pay  all  the  money  I  have,  how  much 
will  I  then  owe  ? 

10.  Lilian  gave  a  $5  hill  in  payment  for  a  pair  of  shoes 
that  cost  $3.75.  How  much  change  did  she  receive  ? 


80  \ITED     STATES    MONEY. 

11.  If  I  have  $6.30,  how  much  more  mon  i  him-, 

to  buy  a  watch  worth  $25  ? 

.'..  A  m. -reliant  bought  broadcloth  at  $3.~~»  a  yurd,  and 
sold  it  at  $5.25.    IIow  much  did  he  gain  on  a  yard  ? 

13.  How  much  will  1»  pounds  of  crushed  SUL: 
17  cents  a  pound  ? 

14.  At  22  cents  a  pound,  how  much  will  :>  pounds  of 
*  raisins  cost  ? 

15.  How  much  will  a  laborer  earn  in  6  days,  at  1 

HrthodM,  pagr   I  ;  »;. 

/' .  How  much  will  8  fruit-knives  cost,  are  25 

,.  \Vhat  will  be  the  cost  of  10  p:ij  is,  at  $.88 

api- 
18.  How  much  will  7  tons  of  coal  cost,  at  $G.:> 

:  8  pounds  of  dried  plums  cost  1  dollar  28  cents, 
what  is  the  cost  of  1  pound  ? 

20.  If  5  yards  of  delaine  cost  $1.85,  how  much  will  1 

1  COSt  ?      Method*,  paffr  1 . ::. 

uhat  ]  :  ill  4  baskets  of  p- 

l.rin.u  *:;.: 

\  gardener  soM  7  bushels  of  sweet-potatoes  for  9 

dollars  80  cents.  What  is  the  price  per  bu^! 

il    -  i       !i  must  I  earn  each  da\ 
10  days? 

?.'f.  If  8  reams  of  paper  cost  $34,  what   is  the  price  per 
ream  ? 

1  90  cents  for  needles,  at  6  cents  a  \ 
How  many  papers  did  she  bi: 

,;>'>.  How  many  pounds  of  rice,  at  8  cents  a  pound,  can 
be  bought  for  2  dollars  24  cents  ?  Method*,  page  / 


COMPUTATIONS.  81 

27.  A  laborer  received  3  dollars,  for  threshing  oats  at  4 
cents  a  bushel.    How  many  bushels  did  he  thresh  ? 

28.  In  one  month  a  young  man  paid  out  $6.50  for 
cigars,  at  10  cents  apiece.    How  many  cigars  did  he 
buy? 

29.  At  9  cents  a  box,  how  many  boxes  of  blacking  can 
be  bought  for  $4.95  ? 

SO.  Amelia  had  1  dollar  42  cents,  but  she  has  paid  out 
56  cents  for  ribbon,  and  37  cents  for  buttons.  How 
much  money  has  she  left  ? 

81.  Hugh  had  84  cents,  his  mother  gave  him  68  cents, 
and  he  gave  96  cents  for  a  hatchet     How  much 
money  had  he  then  ? 

82.  A  gentleman  bought  a  pair  of  gloves  for  $.63,  and 
an  umbrella  for  $1.75,  and  gave  the  shop-keeper  a 
half-eagle  in  payment.    How  much  money  did  he 
receive  in  return  ? 

33.  Luella  bought  8  yards  of  cambric,  at  23  cents  a 
yard,  and  30  cents'  worth  of  machine  twist.    How 
much  did  her  purchases  amount  to  ? 

34.  How  much  will  be  the  cost  of  a  jar  of  10  pounds  of 
butter,  at  28  cents  a  pound,  and  56  cents  for  the 
jar? 

85.  I  bought  a  pound  of  tea  for  $1.62,  and  7  pounds  of 
lard  at  17  cents  a  pound.      How  much  did  my 
purchases  cost  me  ? 

86.  How  much  will  you  have  to  pay  for  9  quires  of 
letter-paper  at  38  cents  a  quire,  and  a  quart  bottle 
of  ink  at  75  cents  ? 

37.  Jason  has  $1.38,  and  he  wishes  to  buy  6  pine-apples, 
which  cost  $.25  apiece.  How  much  more  money 
must  he  have,  to  make  the  purchase  ? 


82  UNITED    STATES    MONEY. 

38.  A  man  bought  8  pounds  of  stove  pipe,  at  19  cei 

i:i«l.  an<l  paid  95  cents.     How  much  did  lu«  then 
owe  upon  it  ? 

How  inm-ii  money  must  be  given,  with  a  kt 
oysters  worth  $1.25,  in  exchange  for  a  turkey  which 
weighs  9  pounds,  at  $.26  a  pound  V 

A  lady  had  27  quarts  of  currants,  and 
$2.48  for  more  at  $.08  a  quart     How  many  <j 
of  currants  had  she  then  ? 

.  Clemen:  s  and  Amos  69  cents,  and  th< -y 

spent  the  whole  of  their  money  for  5  pounc 
almonds.    How  much   did   the  almonds 
poa 

A  grocer  paid  6  dollars  3  cents  for  9  bu 
tomatoes,  and  sold  them  at  85  cents  a  bushel    How 

much  did  lu-  «:ain  mi  a  bushel? 

43.  Viola  paid  $.92  for  pears,  at  $.04  apiece,    A 

inir  i»  of  them  to  Louise,  how  many  had  she  lei 

44.  A  man  who  had  $12,  gave  all  but  $2.10  of 

much  w  ce? 

5  gallons  of  oil  cost  $3.39,  how  run 
Ions  cost? 
Jt'l.  If  10  bushels  of  corn  cost  $8.40,  how  much  will  C 

•  ost? 

of  a  cow  for  7  weeks  costs  $' 
how  much  will  1  rage  cost  for  9  wet 

K   A  paid  $28  for  8  sh  1>  bought  .">  a' 

price.     How  much  did  1?  pay  tor  i 

49.  If  4  m< 

nil  n  earn  in  10  days? 


''"ill  f^~' 

j^S 

-^•^1       CHAPTER   IY. 

jtF 

^^-~v-'    ^*^^**^i^ 

8^4^- 

COMPOUND    NUMBERS. 
#?*$&*** 


SECTION  I. 


"We  determine  the  quantity  of  all  articles  bought  and  sold, 
by  either  measuring,  weighing,  or  counting  them. 

^Denomination  is  the  name  of  the  unit  of  a  concrete  num- 
ber; as,  gallon,  foot,  pound,  hour,  dollar. 

A  ^Denominate  J\~umbcr  is  a  number  applied  to  a 
denomination  ;  a*,  9  quarts,  4  feet,  $7. 

A  Simple  .  1  'umber  is  an  abstract  number,  as,  C,  43,  915; 
or  a  concrete  number  of  but  one  denomination,  as,  78  men,  324 
miles. 

A  Compound  J\*umbcr  is  a  number  expressed  in  two  or 
more  denominations  ;  as,  4  pounds  10  ounces,  15  gallons  3 
quarts  1  pint. 

If  iff  her  Denomination*  are  those  -which  express  the 
greater  amount  or  quantity.  And 

flower  ^Denominations  are  those  which  express  the  less 
amount  or  quantity.  Thus,  a  peck  is  a  higher  denomination 
than  a  quart,  and  a  lower  denomination  than  a  bushel. 

A  ^Denominate  Unit  is  one  of  any  denomination;  as,  1 
pound,  1  foot,  1  quart,  1  dozen. 

In  computations  in  Compound  Numbers,  it  is  often  neces- 
sary to  change  units  of  higher  denominations  to  those  of 
lower,  as  gallons  to  quarts  or  pints  ;  or  units  of  lower  denom- 
inations to  those  of  higher,  as  feet  to  rods  or  miles. 


84  COMPOUND    NUMBERS. 


JHrtioHS  arc  processes  of  changing  numbers  from  one 
denomination  to  another  without  changing  values.  They  arc 
of  two  kinds,  Reduction  Descending  and  Reduction  A»ccn<i 

ftcdnrfioti  •/><.«;»<!>»!/  is  the  process  of  changing  num- 
bers from  higher  to  lower  denominations  ;  and 

Reduction  Ascendinff  is  the  process  of  changing  num- 
bers from  J«  _rher  denominations. 


SECTION  II. 


13.    Liquid  Measure. 

In  im-:isuri:iur  oil.  molasses, 
syrups,    wines,    milk,    and 

otln-r  liquids, 

^- 

*)arelpt   (pint.) 
2  pt.  1  qt    (quart.) 

4  qt.  "   1  gal.  (gallon.) 


1  -rul.  is  4  qt. 
1    qt.      "  2  pt. 

1  pt.    "  4  gi. 


(See  Manual,  p*g«  173.) 

7.    10  gallons  are  how  many  quarts  ?    How  many  pints  ? 
jf.   Change  7  quarts  to  gilla.    M<thod»,  pagt  /;;. 

3.  If  a  pastry-cook  uses  1  gill  of  wine  cv<  h<  »w 
many  days  will  she  use  a  gallon  ? 

4.  In  how  many  days  would  she  use  4  gal.  1  qt.  1  pt. 
3gi.?   JTetfeNte,  ii«  /    /;; 

5.  How  ninny  ]>int  bottles  will  bo  required  to  h 

1.  2  qt  of  tomato  catsup  ? 

6.  A  milk-man  sold  8  .  <>f  milk,  at  8  cr 
quart.     How  much  did  it  amount  to? 

7.  How  many  gallons  arc  82  quarts? 


REDUCTION'S. 


85 


8.  If  you  buy  1  pint  of  milk  a  day,  how  many  quarts 
will  you  buy  in  GO  days  ?  How  many  gallons  ? 

0.  A  druggist  put  up  180  gill  bottles  of  castor-oil. 
How  many  gallons  of  oil  did  he  use  ?  Methods,  P.  177. 

10.  Change  103  pints  to  gallons. 

11.  Reduce  217  pints  to  gallons. 


14. 

Dry 

measure- 

In  measuring 
grain,  seeds, 
fruits,  berries, 
several  kinds 
of  vegetables, 
lime, charcoal, 
and  some  oth- 
er articles, 

2  pt.  are  1  qt. 

8  qt.    "   1  pk.  (peck.) 

4  pk.  "   1  bu.  (bushel.) 

6  quarts  dry  measure  are  equal  to  nearly  7  quarts  liquid 
measure. 

12.  To  how  many  persons  will  a  grocer  sell  8  bushels  of 
apples,  if  he  sells  1  peck  to  each  person  ? 

13.  3  pecks  are  how  many  pints  ? 

L'h  How  many  quart  boxes  will  2  pk.  5  qt.  of  straw- 
berries fill  ? 
7.>.    How  many  pints  are  2  bu.  1  pk.  3  qt.  ? 


1  bu.  is  4  pk. 
1  pk.  "  8  qt. 
1  qt.  "  2  pt. 


86  COMPOUND    NUMBERS. 

16.  A  boy  gathered  3  bushels  4  quarts  of  chestnuts. 
How  many  times  would  they  fill  a  pint  m 
!  low  many  half-peeks  are  9  bushels  2  pecks  ? 

IS.  If  tomatoes  sell  at  3  cents  a  quart,  how  miu 
Imsh.-l  worth  ? 

c  320  pints  to  bushels. 

50.  A  grocer  sold  198  pecks  of  charcoal  in  one 
I  low  many  bushels  did  he  sell  ? 

51.  642  pints  are  how  many  pecks  ?    How  many  bushels  ? 
80,  If  a  boy  sells  ID  quarts  of  jva-nuts  a  day,  how  many 

bushels  will  he  s.'ll  in 
23.   Reduce  59  qua:  >ns. 

.  man  pirkrd  .'JO.')  pints  of 
in  his  garden.     H»w  mai,;. 

15.    Linear  measure. 

In  measuring  distances,  and  th?  dimensions  of  things, — as, 

their  length,  wi.lt h.  thirkn«-ss.  hright,  and  depth.— 


1-:      in.  .!:; 

3     ft  1  >  1   (yard.) 

5.5  or  5J  yd.  "    1  nl.  (rod.) 

320     nl.  "  "    1  mi.  (mile.) 


1  mi.  is  320  r.l. 

1  nl.  "  5.5  or  5^  yd. 

1  yd.  "  8  ft. 

1  ft.    "  12  inches. 


Ami,  in  measuring  goods  sold  by  the  yard  in 


4.5  or  4}  in.  are  1  eighth. 

rhths,  or  9  in.     "    1  qr. 
4  qr.  "    1  yd. 


1  yd.  is  4  qr. 
1  qr.  "  9  in. 
1  eighth  "  4.5  or  4$  in. 


The  first  of  these  lines  is  1  inch  long,  the  second  is  2  inches, 

and  the  third  is  3  inches. 


25.  In  9  feet  are  how  many  inches  ? 

26.  How  many  rods  are  3  miles  ? 


REDUCTIONS 


87 


27.  Change  6  yards  to  feet,  and  4  yd.  2  ft.  to  inches. 

28.  In  43  inches  are  how  many  feet  and  inches  ? 

29.  136  inches  are  how  many  feet  ? 
SO.  Change  92  inches  to  yards. 

31.  How  many  steps,  each  2  ft.  long,  will  James  take  in 

walking  110  yarfls  ? 
J?.  If  a  man  travels  50  rods  in  5  minutes,  how  long  will 

it  take  him  to  travel  a  mile  ? 
83.   35  quarters  are  how  many  yards  ? 

34.  Change  3  yards  2  quarters  to  feet,  and  also  to  inches. 

35.  205  inches  are  how  many  yards  ? 

16.    Square  Xfteasure. 

An  Angle  is  the  difference  of  direc- 
tion of  two  lines  that  meet  in  a  point.  c 

Thus,  ADC  is  an  angle. 

A  'Right- Angle  is  one  formed  by  two  lines  perpendicular  to 
each  other.    Thus,  the  angles  A  D  B  and  ADC  are  right  angles. 


88 


COMPOUND    NCMBEB8. 


A  Surji/cc  is  a  figure  that  has  I<  : 
and  breach  h. 

A  Xectfinffle  is  a  four-sided  figure 
having  only  right  angles.  Thus,  the 
surface  A  B  C  D  is  a  rectangle. 

A  Square  is  a  figure  bounded  by 
four  equal  sicks,  and  having  four  right 


1    ,l,rh    ],,«- 


A  Square  Inch  is  a  square  1  inch 

long  and  1  inch  \\\ 

A  Square  Foot  is  a  square  1  foot 
long  ami  1  i'.M.t  wide; 

A  8f**n  Rod  is  a  square  1  red 
long  and  1  r.»  1  wide;  and 

A  SyiKirc  .  }file  is  a  square  1  mile  long  and  1  mile  v. 

36.  A  blackboard  is  4  feet  wide  and  10  feet  long. 
many  square  feet  of  surface  has  it  ?    Method*,  / 

-,.  IIi.w  many  square  rods  are  there  iii  :  l  rods 

square  ? 
SS.  How  many  panes  of  glass  are  th«-iv  in  a  window 

that  is  4  paiu-s  in  width,  and  G  panes  in  h«  .-iirht  '/ 
39.  What  is  the  number  of  square  inches  on  the  surface 

of  a  mirror  10  inches  long  and  8  incht 
.}'>.  How  many  square  yards  of  carpeting  will  e<>vi  r  the 

floor  of  a  room  6  yards  long  and  5  yards  wide  ? 

41.  The  title  (  -)vcr  of  this  book  was  engraved  on  a  block 
of  box-  wood  4  by  6  inches.    How  much  did  the  wood 
cost,  at  5  cents  per  square  inch  ? 

42.  One  side  of  a  slate  that  is  10  inches  long,  mea 
80  square  inches.    How  wide  is  it  ?     Mftt,o<i*. 

43.  In  drawing  a  map,  Julia  used  a  piece  of  drawing 
paper  »)  inches  loni:.  and  which  contait. 

TI"W  ni.Miy  inch.-s  wid--  \\a-  tl; 


KEDUCTIOtfS. 


89 


44.  The  floor  of  a  bedroom  9  feet  wide  contains  108 
square  feet.    What  is  the  length  of  the  room  ? 

45.  A  school  yard  of  120  square  rods  is  8  rods  wide. 
How  long  is  it  ? 

46.  A  certain  town  is  7  miles  long,  and  it  contains  28 
square  miles.     What  is  its  Width  ? 

In  computing   the  area  of  land,  flooring,  plastering,  and 
other  surfaces, 


144  sq.  in.  (square  in.)  are  1  sq.  ft. 
9  sq.  ft.  "    1  sq.  yd. 

30.25  or  30^  sq.  yd.        "    1  sq.  rd. 
160  sq.  rd.  "    1  A.  (acre.) 

640  A.  "    1  sq.  mi. 


1  sq.  mi.  is  640  A. 
1  A.        "  160  sq.  rd. 


3£  sq.  yd. 

1  sq.  yd. "  9  sq.  ft. 
1  sq.  ft.   "  144  sq.  in. 

47.  3  square  feet  are  how  many  square  inches  ? 
4S.  How  many  square  feet  of  paving  stone  are  there  in 
a  flag-stone  that  measures  3  sq.  yd.  4  sq.  ft.  ? 

49.  How  many  square  rods  are  1  A.  40  sq.  rd.  of  land  ? 

50.  How  many  acres  are  640  square  rods  ? 

51.  36  square  feet  are  how  many  square  yards  ? 

52.  Reduce  121  sq.  yd.  to  square  feet. 

63.  I  low  many  square  inches  are  there  in  a  board  15 

feet  long  and  10  inches  wide  ? 
54.  How  many  square  feet  are  there  on  a  roof  that  is  40 

feet  long  and  20  feet  wide  on  each  of  the  two  sides  ? 
&>.  A  field  16  by  20  rods  contains  how  many  acres  ? 

E  D 

1  /  •   Cubic  Zffeasure*  / 

A  Solid  or  jBody  is  a  figure  that 
has  length,  breadth,  and  thickness. 

A  (Rectangular  Solid  is  a  body 
that  has  six  sides  or  surfacos,  each 


00 


COMPOUND)    NUMBERS. 


of  which  is  a  rectangle.  Thus, 
the  solids  ABCDEFG  and 
MNOPQR8  are  rectangular 
solids. 

A  f  'if>><  is  a  body  that  has  six 
t-«ju;il  sijiuiv  >i'l(  -  <>r  Mil-font 

A  CM  fit*'  ///(-A  is  any  body  or 
u  of  space  1  inch  long,  1 
inch  wide,  and  1  iiu  h  thick. 

A  Cr  >t  has  six  equal 

>ot  square ;  and 

A  CMf'ir  }'(trd  has  six  equal 
surfaces  each  1  yard  square. 

.   II        many  cubic  i; 
arc  tiu  r    in  a  block  1 
long,  6  in.  w  idt •.  and  3  in. 
thick?  117. 

•<:.  \Viiat   ii  the  solidity  of  a 

Mock   of  marble   8 

long,  7  feet   wide,  and  3 

•  thick? 
5S.  How  many  blocks,  rai-li  containing  1  cul)ic  fo< 

be  c-pial  to  a  block  7  feet  long,  nd  4 

59.  A  common  brick  is  2  by  4  by  8  inches.    What  are 
its  solid  contents  ? 

60.  How  long  must  a  box  be,  that  : 

t  thick,  to  contain  72  cu.  ft  ?    Method*. 

: purity  of  a  rectangular  ci-t«-rn  fi  ft.  wide  and 

:>  ft.  diH-ji.  is  -r.n  en,  ft    \\ 

69.  In  dinging  a  cellar  V  nd  1">  y;ir.l<  long, 

1  culiic  yards  of  earth  wore  removed.     ll"'.v  many 
yards  wide  v;:  '.!ar  V 


REDUCTIONS.  91 

In  computing  the  solidity  of  timber,  stone,  portions  of  earth, 
and  many  other  articles,  and  in  estimating  the  capacity  of 
bins,  boxes,  casks,  etc., 


1,728  cu.  in.  (cubic  in.)  are  1  cu.  ft. 


1  cu.  yd.  is  27  cu.  ft. 


1  perch  «)  I"-*  or 
(  lG.Vcu.ft. 


16.5  or  16}  cu.  ft.  "   1  perch. 

27"  cu.  ft,  "   leu. yd. 

'  leu.  ft.  "l,728cu.in. 

63.  In  5  cu.  yd.  are  how  many  cubic  feet  ? 

64.  How  many  cubic  yards  in  81  cu.  ft.  ? 

65.  How  many  cubic  inches  in  1  cu.  ft.  7  cu.  in.  ? 

66.  How  many  cubic  feet  in  2  cu.  yd.  8  cu.  ft,  ? 

67.  What  will  be  the  cost  of  a  piece  of  timber  1  foot 
square  and  20  feet  long,  if  4  cubic  feet  cosfr  $1  ? 

68.  I  low  many  cubic  yards  are  87  cubic  feet  ? 

'>'•'.  How  many  loads  of  earth  of  one  cubic  yard  each, 
must  be  removed,  in  digging  a  cellar  21  feet  long, 
18  feet  wide,  and  6  feet  deep  ? 

70.  How  many  cubic  feet  are  there  in  a  stick  of  timber 
1C  inches  wide,  9  inches  thick,  and  13  feet  long? 

71.  How  many  cubic  blocks,  measuring  2  inches  on  a 
side,  can  be  put  into  a  box  whose  inside  measure- 
ments are  4,  8,  and  10  inches  ? 

72.  How  thick  is  a  block  of  stone  that  is  15  ft.  long  and 
4  ft.  wide,  and  whose  contents  are  180  cu.  ft.  ? 

18.   Wood  Measure. 

In  measuring  wood,  and  also  rough  stone  when  it  is  sold  by 
the  cord, 


16  cu.  ft.         are  1  cd.  ft.  (cord  ft.) 


cd.ft,or)    u 
8  cu.  ft.      J 


,  .  <  128  cu.  ft, 
1CCL  19|or8cd.ft. 
1  cd.  ft.  "  16  cu.  ft. 


Surveyors  of  wood  commonly  call  the  cord  foot  A  Foot  of 


COMPOUND     K  U  M  i;  . 


75.  Htfxv  many  rtiMr  feet  are  5  cord  fc 

-  of  wood  are  how  many  cord  f- 
f.-ct  arc  90  cubic  feet? 

76.  In  47  cord  feet  are  how  many  corda  ? 

.  ;.  A  pOe  of  stone  '•  Mr,  and  4  feet  lii-l 

1  cord.     What  is  its  length  ? 
;  .  How  v.  any  cords  of  wood  are  there  in  a  pile  1 

long,  rj  feet  wide,  and  r,  t\vt  liigh  ? 
;   .  What  cost  5  cords  of  wood,  if  4  cord  feet  cost  3 

doll;. 
80.  How  many  cord  feet  of  wood  in  3  loads,  each  8  feet 

long,  3   fei-t   wide,  and  4  feet  high?     How  many 

cor. 

«v/.  How  many  cords  of  wood  are  1,280  cubic  fe 
..A  pil.'  of  tan  bark   (M-  feet  Ion-.  ide.  and  G 

i  hiirli  contains  how  many  cor,; 


K  E  D  U  C  T I  0  2T  S . 


93 


19.   Weight. 

In  weighing  most  kinds 
of     produce,    provisions,  . 
groceries,  metals,  coal,  and 
many  other  articles, 


16  oz.  (ounces)  are  1  Ib.  (pound.)  1  T.     is   20  cwt. 

100  Ib.  "    1  cwt.  (hundred-weight.)    1  cwt.  "  100  Ib. 

20  cwt.  "    1  T.  (ton.)  1  Ib.     "    16  oz. 

A  barrel  of  flour  weighs  196  Ib.,  and  a  barrel  of  pork,  beef, 
or  fish  200  Ib. 

S3.  How  much  will  1  pound  of  indigo  cost,  at  20  cents 
an  ounce  ?  How  much  will  7  pounds  cost  ? 

84.  At  10  cents  an  ounce,  how  much  will  3  Ib.  8  oz.  of 
nutmegs  cost? 


91  COMPOUND    X  I   M  I!  r. 

85.  II  v,  many  pounds  of  cloves  can  be  bought  for  3 
dollars  8  ;s  an  oui. 

86.  95  ounces  an  Imw  many  pounds? 

87.  1  ' >  pounds  to  In:  ^ht 

ii at  will  7  pounds  G  ounces  of  meat  cost, 
cents  a  ; 

89.  II  'V,  much  will  50  pounds  of  flour  c<  lollars 

:it? 

90.  What  will  -,'  1!).  ii  oa.  of  cheese  cost,  at  ^.lOapound? 
.''/.  How  miu-h  will  ;.»  11  >.  r>  oz.  of  bi:  .  at  $.32  a 

:ul  ? 

•  $10at< 
.'   .  Eow  rnnch  wfll  a  nek  of  flour  n  'imds, 

Co>  in  dollars  a  l'::rr.  1  ? 

'  ;.  \\  : Is  for  $32  a  barr.-l.  lm\v  mr 

pmiiuls  < 
\Vhat  will  ^  T.  1  <  v  ;.  ,,f  hay  cost,  at  $20  a  to- 

inn  flour  sells  at  G  cents  a  pound,  how  much  does 
a  b; 

t  $40  for  5  cwt.  of  iron  castings,  how  much  will  1 
ton  cc.- 

20.   Time. 

In   expressing   port  time  or  duration   of  different 

tangti 
CO  sec.  (seconds)  are  1  min.  (minute.) 


60  min.  are  1  h.     (hour.) 

21  h.  ••    Ida,  (day.) 

"    1  wk. 

\  1  common  yr. 
or  805  da.  (  "  / 

or  366  da. 

100  yr.  "     1  century. 

'  Unual,  page  173.) 


1  century  is  lOOyr. 

, 

loommonyr.-]     , 

i  v,-k.  "       ; 

1.1:1.  "        2  Ml. 

Hi.  "     60  min. 

1  iniu.  u      60  sec. 


REDUCTIONS. 


95 


Every  fourth 
year  from  the 
beginning  of  a 
century  is  a  leap- 
year. 

The  year  is 
divided  into  12 
calendar  months, 
and  these  are  ar- 
ranged in  4  sea- 
sons of  3  mouths 
each,  as  shown  in 
the  diagram  on 
the  next  page. 

February  has 
28  days  in  a  com- 
mon year,  and  29 
in  a  leap-year. 

In  most  busi- 
ness transactions, 
30  days  are  re- 
garded as  a 
month. 

98.  In  3  hours  are  how  many  minutes  ? 

99.  Change  5  minutes  20  seconds  to  seconds. 

100.  How  many  days  are  72  hours  ?     100  hours  ? 

101.  How  many  weeks  are  17  days  ? 

102.  How  many  weeks  are  there  in  July,  August,  and 

September  ? 
1  i-l.  If  a  man  walks  \  mile  in  10  minutes,  how  long 

will  it  take  him  to  walk  12  miles  ? 
I't.'i.  How  many  days  are  there  from  the  7th  of  May  to 

the  4th  of  July  ? 
Jf>~>.  If  a  man  earns  $2  in  6  hours,  how  much  will  he 

earn  in  12  clays  of  10  working  hours  each  ? 


96 


COMPOUND    NUMBERS. 


106.  When  the  sun  sets  at  4  h.  50  min.  P.  M.,  what  is 

th  >f  the  day? 

107.  When  the  sun  rises  at  5  h.  15  min.  A.  M.,  what  is 

length  of  the  night  ?  ,s    Manual.  P.VC  173-> 


lOth 


108.   How  many  weeks  in  1  year  and  17  weeks  ?    How  many 
days? 

'.!'  a  man  earns  $12  a  wivk,  and  pays  $12  a  m«»nth 
for  his  board,  how  many  dollars  will  h.  sn«  in  10 
months,  working  four  ach  month  ? 

110.  How  many  days  in  the  winter  season  ?     In  the 
spring?    In  summer?    In  autumn  ? 


REDUCTIONS.  97 

21.     Faper    and   Counting-. 
In  the  paper  trade, 


24  sheets  are  1  quire. 
20  quires   "   1  ream. 


1  ream  is  20  quires. 
1  quire  "  24  sheets. 


In  counting  several  classes  of  articles  for  market  purposes, 


12  things  are  1  doz.  (dozen.) 
12  doz.       "    1  gro.  (gross.) 


1  gro.  is  12  doz. 
1  doz.  "  12  things. 


Two  things  of  a  kind  are  often  called  a  Pair;  six  things,  a 
Set;  and  twenty  things,  a  Score. 

111.  A  market  woman  sold  G7  cucumbers.    How  many 
dozen  did  she  sell  ? 

112.  If  a  yoke  of  oxen  sells  for  180  dollars,  how  much  is 
one  of  them  worth  ? 

113.  How  many  are  3  score  nud  10  years  ? 

114.  What  is  the  cost  of  6  quires  of  paper,  at  $4  a  ream  ? 
llo.  A  grocer,  in  one  day,  took  in  8  doz.  and  10  eggs. 

How  many  eggs  did  he  take  in  ? 

116.  What  cost  two  gross  of  copy-books,  at  $.10  apiece  ? 

117.  A  silversmith   sold   42  tea-spoons  in  one  week. 
How  many  sets  did  he  sell  ? 

118.  A  shop-keeper  sold,  in  one  week,  2  gross  and  6 
fancy  buttons,  at  ten  cents  a  dozen.    How  much 
did  he  receive  for  them  ? 

119.  A  stationer  paid  2  dollars  a  ream  for  paper,  and 
sold  it  for  18  cents  a  quire.    How  much  was  his 
gain  on  one  ream  ? 

120.  A  grocer  bought  3  pounds  of  nutmegs,  at  128  cents 
a  pound,  and  sold  them  at  10  cents  an  ounce. 
How  much  was  his  gain  ? 

121.  A  market  woman  who  took  5  dozen  of  eggs  to 
market,  broke  3  of  them,  and  sold  the  others  at  24 
cents  a  dozen.    How  much  did  she  receive  ? 

8 


98  COMPOIND     Nl-MDERS. 

SECTION    III. 

A  :/;  '/>  /  /  IOJV. 

1.  Add  7  bushels  1  15  bushels  2  pecks. 

f.  What  i>  tin-  sum  B  5  quarts,  and  1  peck  7  quarts? 

3.  How  many  sq.  yd.  in  the  sum  of  4,  6,  7,  8,  5,  ar. 

4.  A  grocer  sold,  on  Mond  asses ; 
on  Tuesday,  3  gal.  1  «jt. :  and  on  Wednesd; 

2  qt     How  much  did  he  sell?    Method*,  pafff  17*. 

6.  One  week  a  druggist  used  2  gal.  1  «it.  of  al 
and  tli  k  3  gaL  3  qt  1  pt    How  much  did 

he  use  in  ti  ks? 

G.  One  month  a  tailor  used  2  gross  5  dozen  buttons. 
and  in  another  month  3  gross  8  dozen.  Il"\v  many 
buttons  did  he  use  in  the  2  months? 

;.   Ho\v  man;.  n  -.'  li.-lds,  one  contain- 

ing 9  A.  70  sq.  rd.,  and  tin-  other  T  A.  90  sq.  rd.  ? 

5.  A  farmer  sowed  2  bu.  4  qt  of  clover  seed,  and  1  hu. 
:>  j.k.  •;  «jt.  of  timothy  >ord.     How  much  seed  did  IK- 
SOW  of  both  kinds? 

9.  Tin-  foiv  (purlers  of  a  lamb  wished  "t  lb.  0  o;:.  each, 
and  the  hind  (juarters  8  lb.  11  oz.  caeh.  How  much 
did  the  lamb  wei^h  ^ 

.  h:it  is  the  sum  of  2  yd.  2  ft.  9  in.,  and  3  yd.  1  ft.  8  in.  ? 
:  a  laborer  removes  CO  cti.  yd.  13  cu.  ft.  in  di_ 
a  cellar,  and  11  cu.  yd.  19  cu.  ft.  in  digging  the 
drain,  how  much  earth  does  In-  remove? 
/.'.  If  a  fruit  dealer  sells  5  bu.  3  j.k.  of  peaches,  2  b».  1 
pk.  6  qt  of  plums,  and  3  bn.  ;!  pk.  2  qt  of  pears, 
how  much  fruit  does  he  sell  of  the  three  kit, 
.    A   coal  dealer  delivered  13  T.  11  CWt  to  A.  0  T.  i:> 
cwt.  to  B,  and  7  T.  4  cwt. to  ('.    How  nun -!i  o.al  did 
he  sell  to  the  thr- 


SUBTRACT  I  OX.  99 

SECTION    IV. 
s  v%  Tftd.  c  now. 

1.  From  9  bushels  3  pecks  subtract  5  bushels  2  pecks. 

2.  A  grocer  bought  12  Ib.  6  oz.  of  Castile  soap,  and  sold 
5  Ib.  8  oz.    How  much  had  he  left  ?    Methods,  173. 

3.  From  \  bushel  take  £  peck. 

4-  From  6  feet  5  inches  take  4  feet  7  inches. 

5.  On  a  lot  30  ft.  6  in.  wide,  stands  a  house  19  ft.  10  in. 
wide.     How  much  wider  is  the  lot  than  the  house  ? 

6.  From  a  cask  containing  1C  gal.  2  qt.  of  vinegar,  a 
man  drew  8  gal.  3  qt.    How  much  vinegar  remained 
in  the  cask  ? 

7.  A  farmer  sowed  20  bu.  2  pk.  of  wheat,  and  11  bu.  3 
pk.  of  buckwheat.     How  much  more  wheat  than 
buckwheat  did  he  sow  ? 

8.  A  man  removed  42  cu.  yd.  10  cu.  ft.  of  earth  in  dig- 
ging a  cellar,  and  7  cu.  yd.  19  cu.  ft.  in  digging  the 
drain.     How  much  more  earth  did  he  remove  from 
the  cellar  than  from  the  drain  ? 

0.  If  it  takes  9  h.  to  go  from  Albany  to  New  York  by 
steam-boat,  and  5  h.  15  min.  by  railroad,  how  much 
longer  does  it  take  to  go  by  boat  than  by  cars  ? 

10.  When  the  sun  rises  at  5  o'clock  and  40  minutes, 
what  is  the  length  of  the  forenoon  ? 

11.  How  much  of  my  9  weeks'  vacation  is  to  come,  when 
5  weeks  4  days  of  it  have  passed  ? 

12.  From  a  piece  of  land  containing  7  acres,  I  sold  3 
acres  75  square  rods.     How  much  land  had  I  left  ? 

13.  I  bought  a  crock  of  butter  weighing  27  Ib.  9  oz.,  but 
the  crock  alone  weighed  7  Ib.  12  oz.    How  much  did 
the  butter  weigh  ? 


100  COMPOUND    NUMBERS. 


SECTION    V. 

TITL  ZCsi 


1.  Hew  much  tea  will  it  take  to  fill  :.  pnitfent 

ll'iMill^r  VI   1!'.  S  cz.  ?      Method*,  page  /;*. 

a  horee  eats  2  bu.  2  j.k.  4  qt.  of  oats  in  1  week, 
how  much  will  ho  eat  in  4  weeks  ? 

5.  A  painter  used  2  qt  1  pt  of  tu  y  day, 
for  9  days.     How  much  turpentine  did  he  use  ? 

L  2  qr.  of  cassimerc  to  make  on 
of  clothes,  how  miuh  will  it  take  to  make  2  suits? 

1  cow  eat  1  ton  r>  hu  ight  of  hay  in  the 

winter,  how  inueh  will  5  cows  eat  ? 

6.  How  much  paper  will  a  lawyer  use  in  a  year,  at  the 
rate  of  3  quires  7  sheets  per  month  ? 

7.  Oliver  is  7  years  9  months  old,  and  his  moth- 
times  as  old.     How  old  is  his  moth 

S.  How  much  wheat  will  l>e  required  to  seed  3  acres, 

allowing  1  bu.  2  pk.  4  qt  to  the  ai 

a  rail  mad   train  runs  15  miles  80  rods  in  one 

hour,  how  tar  will  it  move  in  4  hours? 
1".  William's  fish  line  is  10  yards  2  feet  long,  and  his 

kite  string  is  10  times  as  long,     llow  long  is  his 

kite  string  ? 
11.  How  many  ste<  ill  be  used  in  a  Commercial 

College  in  8  months,  if  3  gross  7  dozen  are 

monthly  ? 
1  .'.  If  a  farmer  can  plow  2  A.  40  sq.  rd.  of  land  in  1  day, 

how  much  can  he  plow  in  G  days  ? 
13.  How  much  wood  is  there  in  3  piles,  each  pil 

taining  7  cords  12  cubic  feet  ? 


DIVISION.        ***  101 


14.  If  a  family  use  2  dozen  8  eggs  in  a v:eck,  lioiv  ni'aiiy; 

will  they  use  in  4  weeks,  at  the  same  rate  ? 
.75.  If  60  cu.  yd.  15  cu.  ft.  of  earth  are  removed  from 

each  of  two  cellars,  how  much  earth  is  removed 

from  botk  ? 

16.  If  a  painter  uses  2  gal.  2  qt.  1  pt.  of  linseed-oil  in 
painting  1  wagon,  how  much  will  he  use  in  painting 
5  wagons  ? 

17.  What  is  the  weight  of  8  loads  of  hay,  each  weighing 
1  T.  250  Ib.  ? 


SECTION    VI. 

DIVISION. 

1.  IF  a  steam-boat  runs  22  mi.  40  rd.  in  2  hours,  how 
far  does  she  run  in  1  hour  ? 

2.  If  it  takes  13  bu.  3  pk.  of  oats  to  seed  5  acres,  how 
much  does  it  take  for  1  acre  ?    Methods,  page  17  s. 

3.  If  it  takes  5  yards  of  cloth  for  one  military  suit, 
how  many  suits  can  be  made  from  a  piece  contain- 
ing 32  yards,  and  what  remnant  will  be  left  ? 

4.  If  7  men  can  mow  21  acres  35  square  rods  of  grass 
in  a  day,  how  much  can  1  man  mow  ? 

5.  If  a  cooper  can  make  4  barrels  in  5  hours,  how  long 
will  it  take  him  to  make  1  barrel  ? 

6.  If  3  cheeses  weigh  96  Ib.  12  oz.,  what  is  their  average 
weight  ? 

7.  A  grocer  sold  a  barrel  of  flour  to  4  persons,  who 
shared  it  equally.     How  many  pounds  did  each  per- 
son have  ? 

8.  If  a  man  lays  25  rd.  15  ft.  of  stone-wall  in  5  days, 
how  much  does  he  lay  in  1  day  ? 


1  <!  a  fc-P  0  U  X  D    NUMBERS. 


ttmefl'JobiWs.-age  is  42  yr.  9  mo.  -M  ila.     What 
is  his  QL 

10.  A  lady  put  s  qt.  1  pt  1  gL  of  currant  v.  3  bot- 

L     How  much  did  she  put  into  each  bott 

11.  \  man  kill.-d  7  sheep,  and  their  united  u 

280  Ib.  14  oz.     Wliat  was  their  average  weight  ? 
;  '.'  pk.  4  <jt.  of  ch 

tin-in  equally.    How  much  was  each  boy's  sha; 
13.  If  one  apple  liarrel  holds  2  bu.  3  ]>k.,  how  many  bar- 

Ifl  will  be  required  to  hold  11  bu.  of  apples? 
IJf.  A  housekeeper  made  3  gaL  1  qt.  1  pt,  2  gi.  of  cur- 
rant jelly,  and  put   it  up  in  5  jars.     How  much  did 

jar  contain  ? 

/ '.   II«)\v  many  writin.ir-books  can  be  made  from  1  (juire 
d'  foolscap  paper,  allowing  3  sheets  for  each  book? 
1 1   w  many  can  be  made  from  1  n  am  ? 
16.  If  a  railroad  train  runs  80  miles  in  4  hours,  in  how 
many  minutes  will  it  run  1  mile  ? 

man  had  a  pile  of  wood  containing  7  cords  4  cord 
•.  and  he  drew  it  in  5  loads.     How  much  d 
draw  at  a  load  ? 

A  batch  r  kill  d  4  hogs,  whose  united  w 
M  cwt.  40  Ib.    What  was  their  average  weight  ? 
.  A  -sold  •->!  gross  7  dozen  writ  in  g-bo-  ' 

«;  days.     What  wen'  th'-  average  daily  ga'. 

20.  A  man  cut  4  T.  10  cwt.  of  hay  from  3  acres.    What 
was  tin-  average  per  acre  ? 

21.  A  tinsmith  used  3  bu.  3  pk.  of  charcoal  in  8 
What  wafl  the  av.-rage  amount  used  per  da 


REVIEW    PROBLEMS.  103 

SECTION  VII, 


1.  How  many  pint  bottles  will  be  required  to  contain 

3  gal.  3  qt.  of  strawberry  wine  ? 

2.  If  3  pints  of  blackberries  cost  21  cents,  how  much 
will  a  bushel  cost  ? 

S.  Reduce  33  yards  to  rods. 

4-  At  2  cents  an  inch,  how  much  will  2  yards  of  silver 
wire  cost  ? 

5.  A  man  paid  9GO  dollars  for  land,  at  one  dollar  a 
square  rod.    How  many  acres  did  he  buy  ? 

6.  A  stone-mason  laid  up  4  perch  of  stone  in  one  side 
of  a  cellar  wall.    How  many  cubic  feet  did  he  use  ? 

7.  If  4  cord  feet,  or  1  half-cord,  of  wood  cost  2  dollars, 
what  is  the  cost  of  3  cords  ? 

8.  A  grocer  sold  5  quarts  of  cranberries  to  one  person, 
7  quarts  to  another,  and  1  peck  4  quarts  to  a  third. 
How  many  pecks  did  he  sell  ? 

9.  A  lawyer  used  1  ream  of  legal-cap  paper  in  10 
weeks.     How  many  sheets  did  he  use  in  a  day,  on 
an  average  ? 

10.  If  3  eggs  cost  5  cents,  how  much  will  9  dozen  eggs 
cost? 

11.  Which   contains  the   more   land,   a  field   12   rods 
square,  or  a  field  9  by  1C  rods  ? 

12.  From  a  pile  of  wood  containing  7  cords,  a  man  sold 

4  loads,  each  12  feet  long,  4  feet  wide,  and  4  feet 
high.     How  much  remained  ? 

13.  If  you  can  read  5  pages  in  10  minutes,  in  how  many 
hours  can  you  read  a  book  of  150  paires  ? 


104  COMPOUND    NUMBEBS. 

14.  If  a  family  use  5  Ib.  9  oz.  of  butter  in  1  week,  how 
miu-h  will  they  use  ifl  6  week 

A  druggist  has  13  gaL  3  qi  of  alcohol    If  h 

on  an  average,  2  qt  1  pt  a  day,  for  6  dins.  h..\\- 

iniic-h  will  1:  !'t  ? 

nson  has  a  quart  measure  and  a  pin- 

How  many  times  can  he  fill  each  of  them,  sepan. 

from  1  bushel  of  beans  ? 
17.  When  peas  are  worth  ll.GO  a  bushel,  what  will  4 

quarts  cost  ? 
/  .  1 1  ow  much  clover  seed,  at  1  pk.  5  qt  per  acr 

be  rr»|uhvd  to  seed  a  field  of  8  acres  ? 
19.  How  many  rods  long  must  a  field  be,  that  is  20  rods 

wide,  to  contain  3  acres? 
SO.  The  floor  of  a  bedroom  8  feet  wide  is  covered  by  8 

square  yards  of  carpeting.    How  many  feet  long  is 

the  room  ? 
21.  How  many  blocks  2  in< -lit •>  square  can  be  cut  from 

a  piece  of  board  6  by  8  inci 
...  II<>w  many  cords  of  wood  are  there  in  a  pile  12  feet 

long,  4  1*  .  and  8  foot  high  ? 

1 1  MU  mm -h  will  10  Ib.  15  oz.  of  ham  cost,  at  32  cents 

a  pound  ? 

24.  How  many  pounds  of  ground  pepper  will  be  re- 
quired to  fill  100  boxes,  each  box  holding  4  oui. 
v  grocer  sold,  to  5  customers,  6  oz.,  1  Ib.  8  oz.,  12 

oz.,  8  oz.,  and  1  Ib.  4  oz.  of  allspice.   How  much  did 

he  sell  in  all  '! 
26.  How  many  barrels  of  flour  are  there  in  8 

ca^i  containing  49  pounds  ? 
.:.  If  a  family  use  10  pounds  of  pork  P..T  week,  how 

many  wvrk>  will  a  barrel  last  them? 


REVIEW    PROBLEMS.  105 

28.  A  grocer  bought  a  barrel  of  pork,  and  sold,  to  cus- 
tomers, 5  lb.,  8  lb.,  9  lb.,  4  lb.,  6  lb.,  13  lb.,  44  lb., 
and  10  lb.    How  many  pounds  were  then  left  in  the 
barrel  ? 

29.  At  $60  a  ton,  how  much  will  14  hundred-weight  of 
railroad  iron  cost  ? 

30.  A  farmer  bought  2  T.  12  cwt.  of  plaster.    He  sowed 
1  T.  15  cwt.  on  his  wheat  field,  and  the  balance  on 
his  clover  lot.    How  much  did  he  sow  on  the  clover  ? 

31.  A  stationer  bought  a  gross  of  pens  for  72  cents,  and 
sold  them  at  10  cents  a  dozen.     How  much  did  he 
gain  on  1  dozen  ?    How  much  on  the  gross  ? 

32.  At  $.04  a  sheet,  how  many  quires  of  gilt  paper  can 
be  bought  for  81.44  ? 

33.  How  long  is  a  fence  which  incloses  a  piece  of  land 
60  rods  long  and  40  rods  wide  ? 

3.ff.  In  a  year  how  many  days  are  there  in  the  months 
that  have  31  days  each  ? 

35.  A  paper  mill  that  runs  12  hours  per  day,  turns  out 
72  reams  of  print  paper  daily.    How  many  reams  is 
that  per  hour  ?     How  many  quires  per  minute  ? 

36.  How  many  square  inches  are  there  on  one  side  of  a 
common  brick  ?    On  both  sides  ?    On  both  edges  ? 
On  both  ends  ? 

37.  A  grocer  having  8  lb.  of  cinnamon,  sold  to  custom- 
ers 4  oz.,  12  oz.,  6  oz.,  and  8  oz.     How  much  had  he 
left? 

38.  How  many  pint  and  quart  bottles,  of  each  an  equal 
number,  can  be  filled  from  19  gal.  3  qt.  1  pt.  of  cur- 
rant wine  ? 


&#*r>9#- 


^ 

"^**.       . 


M       CHAPTER  Y. 

IUM.'**^-^'^   s-**~< 


FRACTIONS. 


SECTION  I. 


1.  How  many  apples  arc  one  half  of  60  a  j  >]>!.•.>?    One 
third  of  GO  apples  ?    One  fourth  of  CO  apples? 

2.  How  many  dollars  are  one  half  of  $60  ?    One  third 
of  $60  ?    One  fourth  of  $60  ? 

3.  How  many  bushels  arc  one  half  of  60  bushels  ?    One 
t  liird  of  60  bushels  ?     One  fourth  of  60  bushels  ? 

.-  do  you  find  one  half  of  any  number  of  thing*  f      One 
third  f     One  fourth  f     One  fifth  f 

When  an  dollar,  a  bushel, 

or  a  one  of  any  kind,  is  divided  into 
two  equal  parts,  one  of  the  parts  is 
one  half  (})  of  the  one  divi 

When  a  one  of  any  kind  is  divided  into  three  equal  parts, 
one  of  tin-  parts  is  one  third  ($); 

When  a  one  is  divided  into  four  equal  parts,  one  < 
parts  is  one  fourth  (^)  ;  and  so  on. 

When  a  one  is  divided  into  tlmv  c<;uil  parts,  two  of  the 
parts  are  tico  third*  (§)  ;  when  into  four  equal  parts,  two  of 
the  parts  are  two  fourth*  (£),  and  three  of  the  parts  are  three 
fourths  (J)  ;  when  into  five  equal  parts,  one  of  the  parts  is 


DEFINITIONS.  107 

one  fifth  (|),  two  of  the  parts  are  two  fifths  (£),  three  of  the 
parts  are  three  fifths  (f ),  and  four  of  the  parts  are  four  fifths  (|). 

When  a  one  is  divided  into  six  equal  parts,  the  parts  are 
sixths;  when  into  seven  equal  parts,  they  are  sevenths;  when 
into  eight  equal  parts,  they  are  eightlis;  when  into  nine  equal 
parts,  they  are  ninths ;  when  into  ten  equal  parts,  they  are 
tenths;  and  so  on. 

Each  of  the  numbers  fa  fa  fa  fa  and  so  on,  expresses  one  of 
the  equal  parts  of  a  one. 

The  number,  f  expresses,  either  that  2  is  divided  into  3 
equal  parts ;  or  that  1  is  divided  into  3  equal  parts,  and  2  of 
those  parts  are  taken. 

5.  What  does  the  number  |-  express  ?    What  the  number  £  ? 

6.  What  does  the  number  f  express  ?     The  number  £  ? 

7.  What  is  expressed  by  the  number  $  ?    By  f  ?    By  ^  ? 

8.  What  is  expressed  by  the  fraction  f  of  an  apple  ? 

9.  What  do  you  understand  by  $f  ? 

10.  Explain  the  meaning  of  79g  lb.,  and  ^  doz. 

A  Fractional  Unit  is  one  of  the  equal  parts  into  which 
a  thing,  or  the  unit  1,  is  divided :  as,  fa  £,  fa  fa  and  so  on.  And 

A  Fraction  is  a  number  consisting  of  one  or  more  frac- 
tional units  :  as,  fa  f ,  $£,  ^  lb. 

11.  What  is  the  fractional  unit  of  *}  ?   Of  J  ft.  ?   Of  |  lb.  ? 
7,?.  What  is  the  fractional  unit  of  J  yd.?    Of  {•}  bu.? 

OfJfecwU 

The  Terms  of  a  fraction  are  the  two  numbers  used  to  ex- 
press it.  Thus,  the  terms  of  the  fraction  £  are  5  and  7. 

The  ^Denominator  of  a  fraction  is  that  term  which  ex- 
presses the  number  of  equal  parts  into  which  one  is  divided ; 
it  is  written  below  the  horizontal  line. 

The  Numerator  is  that  term  which  expresses  the  number 
of  equal  parts  indicated  by  the  fraction ;  it  is  written  above 
the  line.  Thus,  in  the  fraction  fa  the  5  is  the  denominator, 


108  FRACTION 

and  expresses  that  1  is  divided  into  5  equal  parts ;  a: 

1   i-  tii«    Hum*  rator.  and  expresses  that  4  of  the  equal 
(fifths)  are  indicated  by  the  fraction. 

15.  What  are  the  terms  of  the  fractions  f ,  f ,  fa  and  ff  t 

L'f.  Wh:it   i-i  tlu-  denominator  of  each  of  the  fractions},-,^, 
^ J,  and  ,'y,  and  what  does  it  express  t 

uerator  of  each  of  the  fractions  |,  -,V  f, 
and  |f,  and  what  does  it  express  ? 

16.  Namo  the  terms,  the  denominator,  the  numerator, 
the  fractional  unit,  and  the  number  of  fractional 
units  in  T70.    In  f  mi.     In  }  eq.  yd.     In  ?•.  gaL 

A  Proper  /-'/-action  is  a  fraction  whose  value  is  less  than 
1 ;  as  |,  T^,  {,  Jf.     Its  nu:  always  less  than  its  dc- 

nonni: 

An  Jiniir<.;.>-r  t&octio*  !••  i   i    i^n  whose  Talue  equals 
1  ;  as  f,  fj,  l»  H»  IJ-     Ite  numerator  is  never  less 
than  its  denomh 

xii/u'ltir  /•*r(irt;<>Hs  arc  those  that  have  a  common  frac- 
tional unit  ;  as,  \  and  {;  |,  I,  and  |. 

The  dcnominutors  of  similar  fractions  are  alike.     Such  frac- 
tions are  said  to  have  a  Common  Denominator. 
•  si itiil ft r  /-'rncfinnt  are  those  that  lur. 
tional  units ;  as,  }  and  f ;  f ,  f ,  and  \. 

17.  If  •">  apjiK'S  are  di- 
vided e<|uall\ 
twreii   *J  elii'. 
what  part  of 
apples    will    each 
child  h:i 

18.  How  many  apples  must  be  cut  into  equal  par 

19.  If  5  apples  are  divided  equally  between  •„»  cbi 
how  many  apples  will  each  child  receive? 

20.  If  I  divide  8  pears  equally  amon.ir  X  girls,  how  many 
whole  pears  can  I  izive  to  each  pirl  ? 


DEFINITIONS. 


109 


21.  Into  what  equal  parts  must  the  other  pears  be  cut  ? 
J.?.  How  many  of  these  equal  parts  will  there  be  ? 
,.'-A  If  I  divide  8  pears  equally  among  3  girls,  how  many 
pears  will  each  girl  receive  ? 

One  lemon  is  what  part 


24.  Of  2  lemons  ? 

25.  Of  3  lemons  ? 

26.  Of  5  lemons  ? 


27.  Of  7  lemons  ? 

28.  Of  10  lemons  ? 
£9.  Of -15  lemons? 


What  part  of 


SO.  1  doz.  oranges  is  1  orange  ? 

31.  1  ft.  is  1  in.  ? 

32.  1  Ib.  is  1  oz.  ? 


,    3|, 

tfo 

,    A. 


?.  1  qt.  is  1  pt.  ? 
££.  1  gal  is  1  pt.  ? 
85.  1  yd.  is  1  in.  ? 

When  a  number  is  expressed  by  an  integer  and  a  fraction, 
it  is  a  Mixed  Number;  as,  8|,  llf,  14|$. 

56'.  Which  of  the  fractions  in  the  margin  are 
proper  fractions,  and  why  ? 

87.  Which  are  improper  fractions,  and  why  ? 

88.  Which  are  mixed  numbers,  and  why  ? 

39.  Which  are  similar  fractions,  and  why  ? 

40.  Which  are  dissimilar  fractions,  and  why  ? 

41.  What  do  you  understand  by  1  half  of  any  number  or 
thing  ?    By  1  third  ?     1  fourth  ?     1  fifth  ?     1  eighth  ? 

42.  What  do  you  understand  by  2  thirds  of  any  number  or 
thing  ?     By  3  fifths  ?     By  7  eighths  ? 

43.  What  do  you  understand  by  2  halves  of  any  number  or 
thing?     By  f?     By  |?     By  f  ?     By  £  ?     By  £  ? 


*, 


110  FRACTIONS. 

SECTION    II. 


22.   Fractions  to  Lowest  Terms. 

1.  IF  a  pie  be  cut  into  10  equal  parts,  what  will  one  of 

th.  parts  be? 
..  Into  how  many  fifths  can  a  pie  be  cut  ?     Into  how 

many  halves? 

£.  ||  are  how  many  fifths  ?    How  many  halves  f 
.;.  How  many  fifths  of  a  pie  are  there  in  ^  ?    In  -,<0  ? 

In  ,".. 


5.  Reduce  -&  to  halves. 

6.  f  of  a  melon  are  how  many  halves  ? 

7.  |  of  a  melon  are  how  many  fourt 

8.  T88  of  a  melon  are  how  many  eighths  ?    IIow  many 
fourths  ?    How  many  halves  ? 

9.  Change  |4  of  a  cubic  yard  to  thirds.    Method*,  pay 

10.  £%  of  a  dollar  are  how  many  tenths  ?    How  many 

fifths? 

/  /.  :l  I  of  a  dollar  are  how  many  fifths  ? 
12.  Reduce  VfcV  to  sixtieths.     To  thirtieth?.     To  fiftee* 
IS.  Dividing  both  term*  af  a  fraction  by  the  tame  numfcr,  hat 
fffcct  upon  the  value  of  the  fraction  f 


REDUCTIONS.  Ill 

When  the  terms  of  a  fraction  have  no  common  factor,  they 
are  2>rime  to  JZach  Ofhc>\ 

A  fraction  is  in  its  Z,owest  Terms,  when  its  terms  are 
prime  to  each  other. 

14.  Reduce  &  to  its  lowest  terms.    Methods,  page  17 8. 

15.  What  are  the  lowest  terms  of  the  fraction  &$  ? 

16.  Reduce  the  fractions  fa  and  T«T  to  their  lowest  terras. 

17.  Reduce  fa  and  f£  to  their  lowest  terms. 

18.  Reduce  ff  and  £ f  to  their  lowest  terms. 

19.  James  has  g  of  an  apple,  and  Charles  has  -ft.   Which 
has  the  greater  fraction  ? 

20.  Which  is  the  greater  sum  of  money,  $3fi0  or  $|80  ? 

21.  Andrew  dug  5  rows  of  potatoes,  which  yielded  re- 
spectively £  bu.,  )-f  bu.,  £f  bu.,  T82  bu.,  and  4i  bu. 
Which  row  gave  the  greatest  yield  ? 

22.  Reduce  ||,  f£,  and  f|  to  their  lowest  terms. 

23.  Fractions  to  Given  Denominators. 

23.  If  a  pie  is  cut  into  10  equal  pieces,  how  many  of 
these  pieces  will  there  be  in  one  half  of  the  pie  ? 
How  many  of  these  equal  pieces  will  there  be  in  I 
of  the  pie  ?     Jf  ow  many  in  §  of  it  ?     In  |  ?     In  |  ? 

25.  Reduce  |,  f ,  £ ,  and  £  to  tenths. 

26.  1  half  of  an  apple  is  how  many  quarters  or  fourths  ? 
1  third  of  a  pear  is  how  many  sixths  ? 

28.  How  many  eighths  of  a  bushel  is  j  bu.  ? 
20.  Change  J  of  an  hour  to  fifteenths  of  an  hour. 
80.  2  thirds  of  a  pear  are  how  many  sixths  ? 

31.  How  many  eighths  of  a  bushel  are  |  bu.  ? 

32.  Reduce  jj  Ib.  to  sixteenths.     Methods,  page  173. 

.  Reduce  £  to  eighths.     To  twelfths.     To  twentieths. 
84.  How  many  twenty-fourths  are  £?     How  many  are  f  ? 
Are     ?       ?       ?         ? 


11.'  FRACTIONS. 

S5.  Multiplying  loth  term*  of  a  fraction  ly  the  same  number  hat 
what  effect  upon  the  value  of  the  fraction  t 

36.  $  equals  how  many  tenths  ? 

37.  By  what  number  will  you  multiply  the  terms  of  the  frac- 
tion 'I,  to  rediic-  it  t<»  t \\vntv-lifthst 

38.  Reduce  1 1 

low  may  fourths  be  reduced  to  twentieths?    Eighths  to 

fortieths  ? 
40.  What  is  the  least  denominator,  greater  than  :'.  to  which 

thirds  can  be  reduced  ?    Why  ? 
/,/.  Xame  the  first  three  denominators,  in  order  of  size,  to 

which  fifths  can  be  redi: 
43.  Why  can  fifths  be  reduced  to  each  of  these  denominators  ? 

43.  jf  any  fraction  it  reduced  to  an  equal  fraction,  h<i 
greater  denominator,  what  mutt  that  denominator  le  f 

44.  Reduce  to  i  ft.,  and  |  It. ;  J  doz.,and 

45.  Reduce  }  A.  an  1     A.  i  -  i\\  mieths  of  an  acre? 

IttBgQ  as  many  as  possible  of  tli>-  following  fnic- 
tijns  to  twenty-fourths:  j  da.,  f  da.,  $  da.,  T7f  da^ 
T^  da>,  ft  dm  A  **"  a»d  A  da, 

47.  What  fraction*  can  T*  reduced  to  a  given  denominator? 

48.  How  may  f  be  rolucr.1  to  fortieths  ? 

49.  How  may  ^  be  reduced  to  one  hundred  forty-sevenths  ? 
60.  Reduce  $J,  $],  $J,  $r'0,  l^and  $^3  to  hundredtha. 

24.   Dissimilar  Fractions  to  Similar  Fractions. 
51.  Reduce  }  and  f  to  sixtlis. 
5$.  Change  f  and  f  to  twelfths;  and  f  and  \  to  thirty.fifthfi. 

53.  Reduce  |,  f,  and  |  to  ninetieths. 

54.  In  the  results  in  the  three  preceding  problems,  the  com- 
mon denominator  of  the  sin  ions  is  the  pr< 

of  what  terms  .' 

55.  What  is  the  common  denominator  of  the  similar  fra 
to  which  J,  *,  and  f  may  be  rediu 


REDUCTIONS.  113 

56.  In  solving  problem  55,  by  what  numbers  must  the  terms 
of  £  be  multiplied  ?     The  terms  of  £  ?     Of  f  ? 

57.  Li  reducing  dissimilar  fractions  to  similar  fractions,  by  what 
must  the  terms  of  each  given  fraction  be  multiplied  f 

58.  Reduce  f  and  f  to  similar  fractions. 

59.  Reduce  f  and  $  to  similar  fractions.     Methods,  page  178. 
CO.  What  similar  fractions  are  equal  to  T\-  and  |  ? 

61.  Change  ^,  \,  and  ^f  to  similar  fractions. 

62.  Reduce  £  and  T8S  to  fractions  of  the  same  fractional  unit. 

63.  Reduce  £,  £ ,  $,  and  -J  to  similar  fractions. 

64.  Reduce  the  same  fractions  to  similar  fractions  having  72 
for  a  common  denominator.    Reduce  them  to  forty-eighths. 

65.  Reduce  the  same  fractions  to  twenty-fourths.    To  twelfths. 

66.  What  fractions  can  be  reduced  to  twelfths  ?     Why  ? 

67.  Which  of  the  fractions  $,  {.,  f ,  f,  and  £  can  be  reduced  to 
eighteenths,  and  which  can  not  ?     Why  ? 

68.  What  fractions  can  be  reduced  to  equal  fractions  Jiaving  a 
given  denominator  f 

69.  Wftat  is  the  denominator  of  the  least  similar  fractions  to  which 
any  two  or  more  given  fractions  can  be  reduced? 

70.  What  are  the  denominators  of  the  fractions  which  can  be 
reduced  to  fifteenths  ?     To  sixteenths  ?     To  twentieths  ? 

71.  What  fractions  can  be   reduced   to   thirty-ninths  ?     To 
sixty-fourths  ?     To  eighty-firsts  ?     To  two  hundredths  ? 

72.  Reduce  £,  £,  £,  and  -J  to  least  similar  fractions. 

73.  Reduce  ~  cu.  yd.,  £$  cu.  yd.,  and  J  cu.  yd.  to  least 
similar  fractions. 

74.  What  is  the  common  denominator  of  the  least  similar 
fractions  equal  to  the  fractions  £,  ^,  and  -*-£  ?     What  are 
the  new  numerators  ? 

75.  Reduce  |,  f ,  -/s,  and  -&  to  least  similar  fractions. 

76.  What  is  the  fractional  unit  of  the  least  similar  fractions 
equal  to  ^,  ^,  ff,  and  £  ? 

77.  What  are  the  least  similar  fractions  ? 


1H  PBACTIOXS. 

78.  Change  ft, If  f ,  ft,  iV,  <"»<!  A  to  least  similar  fractions. 
What  is  the  least  common  fractional  unit  ? 
Iteduce  |,  f  and  |  to  least  similar  fractions. 

25.   Improper  Tractions  to  Integers  or  Mixed  Numbers. 

SO.  How  many  dollars  arc  2  halves  of  a  dollar  ?    5  fifths 

of  a  dollar?     8  eighths  of  a  doll- 
81.   When  i*  the  talue  of  a  fraction  a  onef     11 

.  A  boy  has  4  half-dollars.    How  many  dollars  has  he  ? 
83.  A  girl  buys  12  fourths  of  a  yard  of  ribbon.     ! !  m 
many  yards  does  she  1 
I < >w  many  feet  are  J  of  a  foot  ?    Method*,  p«v. 

85.  How  many  dozen  are  3G°  of  a  do; 

86.  Reduce  V  gaL  to  gallons. 

87.  A  barber  receives  5  half-dollars  for  each  day's  work. 
How  much  are  his  daily  wages  ? 

88.  One  week  a  cook  used  J  of  a  gallon  of  syrup.     II   « 
many  gallons  did  she  use  ? 

.v.  A  tailor  used  *g<  yd.  of  beav  in  making  an 

overcoat  How  many  yards  did  he  use  ? 

90.  One  day  a  confectioner  sold  63  quarter-pound  pack- 
ages of  candy.  How  many  pounds  did  he  sell  .' 

01.  Reduce  J57  min.  to  minutes. 

92.  Reduce  -if*  to  a  mixed  number. 

03.  ff  are  how  many  ones  ? 

04.  Change  .41,  ^  A|i,  and  |J  to  integers  or  mixed  numbers. 

26.    Integers  or  Mixed  Numbers  to  Fractions. 

•  ' ".  II"\v  many  Iialf-Kanvis  can  bo  filled  with  3  barrels 
of  flour  ? 

96.  How  many  tenths  of  a  dollar  are  7  dollars  ? 

97.  Reduce  9  yards  to  fourths.    To  eighths. 


REDUCTIONS.  115 

98.  Reduce  27  to  fifths.     To  ninths. 

99.  Reduce  8|  to  ninths.     Methods,  page  179. 

100.  How  many  eighths  of  a  cord  of  wood  in  2|  cords  ? 

101.  How  many  quarter-dollars  will  it  take  to  pay  for  a 
fur  cap  that  costs  $6|  ? 

102.  How  many  half-yards  are  one  rod  ?     How  many 
half-feet  ? 

103.  5 1  tons  of  hay  are  how  many  fifths  of  a  ton  ? 

104.  How  many  sixteenths  of  a  pound  are  3T9<j  pounds 
of  butter  ? 

105.  Reduce  27T3<j  A.  to  tenths  of  an  acre. 

106.  Reduce  29£  and  7-&V  *°  improper  fractions. 


SECTION    III. 

ADDITION. 

1.  A  MOTHER  having  a  melon,  gave  2  ninths  of  it  to 
her  boys,  and  5  ninths  of  it  to  her  girls.    How  many 
ninths  of  the  melon  did  she  give  to  her  children  ? 

2.  A  teamster  feeds  his  horses  §  of  a  bushel  of  oats  in  the 
morning,  f  at  noon,  and  |  at  night.     How  many 
eighths  of  a  bushel  does  he  feed  his  horses  daily  ? 

3.  A  lady  paid  $r30  for  eggs,  and  8-,%  for  butter.    How 
much  did  the  butter  and  eggs  cost  her  ? 

4.  Cynthia  paid  $J  for  a  pair  of  gloves,  $f  for  a  hand- 
kerchief, $|  for  a  neck  ribbon,  and  $§  for  a  collar. 
How  many  dollars  did  she  expend  ? 

5.  How  many  hours  are  f  h.,  I  h.,  £  h.,  and  f  h.  ? 

6.  What  is  the  common  fractional  unit  of  -f ,  f ,  |,  and  %  ? 

7.  How  many  fractional  units  does  each  of  these  fractions 
express? 


110  FRACTIONS. 

8.  lie  sum  of  these  fractional  units  f 

9.  How  are  similar  fraction*  added  t 

10.  What  similar  fractions  are  equal  to  $£  and 

11.  What  is  the  sum  of  these  similar  fractions? 

1  $i  for  • 

bagc.    How  much  did  she  pay  for  both  ? 
13.  My  door-yard  contains   {   A.,  ami  my  pardon  J  A. 

I  I«»w  much  land  in  my  door-yard  and  gard« 
14*  Roger  worked  T70  h.  to  saw  his  wo<>  h.  to 

split  it.     I  low  many  hours  did  he  work  't 
.''.  A  !,i;ni  i  «•:;•  |  of  his  meadow  one  day,  «: 

1 1  day.    How  much  of  it  did  he  cut  in  the 

tWO  days  ?       Jrr//io<**,  page  i 

16.  A  .s  I  A.  of  tomatoes,  and  f  A.  of  cu- 

cumbers.    How  much  land  has  he  planted  to  l>« 
Vh:it  U  t  he  sum  off  and  {?     Of^Endf! 

28.  Add  |  and  f;  also  |  an.: 

In  adding  diuimilarfactivnt,  what  it  the  first  ricpt 

SO.   What  it  the  second  ttep? 

21.  During  a  campaign  ^  of  a  regiment  werv  k  i 

wi-iv  wounded,  and   \  were  taken  prisoners.     What 
]>urt  uf  the  ivLrinu-nt  was  lost  to  the  sen 

. .'.  Id;i  bought  a  box  of  figs,  and  gave  £  of  them  t 
father,  |  of  tin-in  to  lu-r  mother,  and  7'0  of  them  to 
her  sister.    What  part  of  them  did  she  giv. 
.    LevigavcfcJ  f«>r  his  skates,  $^  for  the  > traps  fur  th- in, 
and  $5  f°r  nis  sled-     How  much  did  all  cost  him  ? 

':-.  I^arnct  has  £  mi.  of  rail  fence  on  his  fa- 
mi.  of  board  fence,  and  T70  mi.  of  stone  fence.     How 
much  fence  is  there  on  his  farm? 

2J.  A  lawyer  used  T7¥  of  a  quire  of  1  paper  on 

Monday,  §  of  a  quire  on  Tuesday,  §  of  a  quire  on 


ADDITION.  117 

"Wednesday,  £  of  a  quire  on  Thursday,  and  |  of  a 
quire  on  Friday.     How  much  paper  did  he  use  ? 
26.  What  is  the  sum  of  $,  T\,  and  £  ? 


27.  Add  £,  |,  and  f 
**.  Add  ^F,  f  and  f 


#9.  Add  |-,  |,  and  f . 
SO.  Add  |,  £,  A,  and  f. 


31.  Hattie's  age  is  6}  years,  Jennie's  age  is  5J  years,  and 

the  age  of  their  brother  Harry  is  3  ^  years.     What 

is  the  sum  of  their  ages  ? 
82.  A  merchant  sold  2  bu.  of  clover  seed  to  one  farmer, 

I  bu.  to  another,  and  |  bu.  to  a  third.     How  much 

did  he  sell  to  all  of  them  ? 
33.  A  teamster  drew  J  cd.  of  wood  at  one  load,  and  1  \ 

cd.  at  another  load.    How  much  wood  did  he  draw  ? 
84.  A  mechanic  earned  $H  in  the  forenoon,  and  $1|  in 

the  afternoon.     How  much  did  he  earn  in  the  day  ? 
35.  Jonas  gave  82.J  for  a  sheep,  and  sold  it  for  $T70  more 

than  it  cost  him.     For  how  much  did  he  sell  it  ? 
86.   What  is  the  sum  3£  of  and  G  j  ? 


37.  Add  15f  and  8f  ? 

38.  Add  4&  and  |  ? 

39.  Add5and7TV 


40.  Add  6,  2£,  and  f 

41.  Add  18^4-  and  7f. 
4#.  Add  5|,  7£,  and  4 


£?.  A  man,  in  trying  the  speed  of  his  horse,  trotted  him 
one  mile  in  2T7^  min.,  a  second  mile  in  2|  min.,  and 
a  third  mile  in  2.J  min.  In  how  many  minutes  did 
the  horse  trot  the  three  miles  ? 

44*  In  a  city  are  four  street  railroads,  one  3 \  mi.  long,  an- 
other 2T90  mi.  long,  another  4  J  mi.  long,  and  the  fourth 
If  mi.  long.     What  is  the  length  of  all  of  them  ? 
What  is  the  sum 

45.   Of  f  2f ,  and  17  ?  \  47.   Of  2|,  4|,  and  3f  ? 

4£   Of  I,  £,  ±,  and  |  ?  I  48.   Of  8*,  2fc  4f ,  and  6  ? 


118  FRACTIONS. 

SECTION   IV. 


1.  AMANDA  cut  f  of  a  yard  of  silk  from  a  pi.  -re  that 

contained  J  of  a  \a:  ••!.     How  many  ei-hths  of  a  \ard 

of  silk  were  left  111  the  piece? 
•han  gathered  j,1.  liu.  of  walnuts,  and  sold  all  hut 

T48  bu.  of  them.     IIow  many  did  he  sell  ? 
8.  From  -^  subtract  ^. 
4'  One  forenoon  a  man  sawed  I  cd.  of  wood,  and  his 

son  sawed  j  cd.     How  much  more  did  the  fat  In  -r 

saw  than  the  son  ? 
'/'if  ard  similar  fraction*  subtracted  f 

6.  What  similar  fractions  are  equal  to  $|  and  $]  ? 

7.  Find  thf.  difference  between  these  similar  fraci 

8.  Gerald  having  $f,  gave  $3  for  a  slate.     H><\\ 
money  had  he  left?     Method*,  pagr  r,  >.>. 

9.  What  is  the  difference  between  f  and  f  ? 

7fl.  A  dniggist  poured  ^  gaLof  alcohol  from  a  jr.. 

contained  £  gaL    How  much  alcohol  was  left  ? 
11.  It'  I  have  a  village  lot  of  f9  A.,  and  I  sell  ^F  A^  how 

large  a  lot  shall  I  have  left? 
.   A  in-  reliant  hin  <  ui-l;i-  .  and  sells  it  at  $J  J 

a  gallon.     How  muuh  is  his  gain  per  gallon  ? 
IS.  I  —  -fa  =  what  number  I 

14.  |.  —  |-  =r  what  number  ? 

15.  What  is  the  <lit;  J  and  ^? 

16.  In  subtracting  difiirni  <s,  icJiat  u  tltcjirst  ttup? 

17.  What  it  the  second  step  f 

1^.  Eli  paid  4  of  the  cost  of  a  sled,  and  Carlos  paid  the 
rest     How  much  of  the  cost  did  Carlo-  ]•;-. 


SUBTRACTION.  119 

19.  Anna  will  be  13  years  old  in  f  of  a  year.     How  old 

is  She  nOW  ?      Methods,  page  179. 

20.  A  housekeeper  bought  2  bu.  of  potatoes,  and  used  f 
bu.  the  same  day.    How  many  had  she  left  ? 

21.  If  I  buy  a  hammer  for  l/^,  and  I  give  in  payment  a 
5-dollar  bill,  how  much  change  shall  I  receive  ? 

S3.  30  is  how  much  more  than  •£  ? 

23.  A  grain  buyer  paid  $lf  a  bushel  for  wheat,  but  was 
obliged  to  sell  it  at  a  loss  of  $J  a  bushel.    At  what 
price  did  he  sell  it  ? 

24.  A  gardener  raised  11 J  bu.  of  beans,  and  sold  T\  bu. 
How  many  had  he  left  ?    Methods,  page  170. 

25.  I  owe  $5A ;  if  I  pay  $J,  how  much  shall  I  then  owe  ? 

26.  4T5ff  is  how  much  greater  than  £  ? 

27.  64-j^  is  how  much  greater  than  f  ? 

28.  What  is  the  difference  between  Cf  and  4;  .; 

20.  If  I  have  $5  J,  and  I  pay  $21  for  a  pair  of  fur  gloves, 
how  much  money  shall  I  have  left  ? 

30.  A  laborer  who  earns  $8|  a  week,  expends  $G  j.    How 
much  does  he  save  weekly  ? 

31.  From  a  cask  of  vinegar  containing  32*  gal.,  a  clerk 
drew  5 -J  gal.    How  much  vinegar  was  left  in  the  cask  ? 

32.  A  butcher  sold  9T5ff  Ib.  from  a  quarter  of  beef  that 
weighed  93 1  Ib.     How  many  pounds  had  he  left  ? 

33.  A  man  traveled  161  mi.  in  the  forenoon,  and  31  f  mi. 
in  the  day.    How  far  did  he  travel  in  the  afternoon  ? 

34.  From  17TV  subtract  4£. 

85.  25|  is  how  much  greater  than  6T47  ? 

36.  6  is  how  much  greater  than  4£  ? 

37.  From  a  box   containing  10  pounds   of  raisins,  a 
grocer  sold  4|  pounds.     How  many  pounds  of  rai- 
sins were  left  in  the  box  ? 


130  FRACTIONS. 

SECTION   V. 


Ml'  f. 

27.     A  Traction  by  an  Integer. 

1.  1  low  many  seven  1  1  1  :  i  mcs  1  se  ' 
of  a  week  ? 

2.  IIow  many  fifths  of  a  dollar  arc  G  times  2  fifths  of  a 
dolh  r  I     II"  \v  many  dollars  ? 

£.  How  much  will  6  bushels  of  apples  cost,  at  $|  per 

bushel  ?       Method*,  pagr  170. 

.'.  i  low  many  acres  of  corn  can  G  men  hoe  in  a  <!. 

they  average  J  of  an  acre  each  '' 

Bow  much  will  12  11).  wool  cost,  at  $fj  a  pound  ? 
'      What  effect  it  produced  by  multiplying  the  numerator  of  a 

fraction  by  an  integer  J 

7.  Multiply  2  1 

8.  What  is  the  product  off}  multiplied  by  7? 

9.  How  much  is  28  times  5  sq.  yd.  of  carp<  t  i 
JO.  What  part  of  5  bushels  is  1  busln  1  ? 

11.  What  part  of  5  bushels  are  2  bushels?    Are  3 

.   .  A  L  -.::•,;.  :.  r  bought  ."»  (jt.  of  Early  Kent  peas.    AVhat 

part  of  a  pock  did  he  l»uy  ? 

/  ..  A  fanner  having  a  bushel  (or  5G  Ib.)  of  coarse  salt, 
used  28  Ib.  of  it  in  packing  a  barrel  of  beef.     V 
part  of  a  bushel  did  he  use  to  the  barrel  ': 
What  part  of 


14.  C  yd.  arc  5  yd.  ? 

0  pailfuls  arc  4  pailfuls  ? 

16.  25  bar.  are  9  bar.  f 

17.  12  candles  are  8  candles? 


18.  1  gal.  are  2 

pk.  arc  4  qt.  ? 
SO.  1  mi.  are  240  rd.  ? 
21.  1  Ib.  are  6  oz.  ? 


J.'.  If  :»  boy*  share   :5   bushels  of  butternuts  equally, 
what  part  of  a  bushel  has  each  boy  ': 


MULTIPLICATION.  121 

28.    A  Mixed  Number  by  an  Integer. 
£9.  How  much  milk  will  be  required  to  fill  3  pails,  each 

of  which  holds  2J  gallons  ? 
24.  How  much  will  15  barrels  of  XX  flour  cost,  at  $7T7a 

per  barrel  ?    Methods,  page  179. 
2-5.  A  sheriff,  in  pursuing  a  thief,  drove  ?g  miles  an 

hour  for  5  hours.     How  many  miles  did  he  drive  ? 
20.  A  grocer  bought  one  dozen  boxes  of  layer  raisins,  at 

$1T75  per  box.     How  much  did  he  pay  for  them  ? 
27.  5  times  6TS¥  =  how  many  ?     50  times  4'-  —  how  many? 

29.    An  Integer  by  a  Fraction. 
,>'.  When  G  Ib.  of  crushed  sugar  sell  for  $1,  how  much 

does  1  pound  cost  ? 
29.  When  wood  is  $5  a  cord,  how  much  must  I  pay  for 

£  Of  a  COrd  ?      Methods,  page  179. 

How  much  is 


30.  1  fourth  of  3  yd.  ? 
81.  1  seventh  of  5  da.  ? 
32.  1  twelfth  of  7  A.  ? 


33.  TV  of  6  dimes  ? 

34.  &  of  24  bu.  ? 

35.  of  24  h.  ? 


36.  If  a  man  lays  44  rods  of  stone-wall  in  5  days,  how 
many  rods  does  he  lay  in  1  day  ? 

37.  A  farmer  raised  150  bushels  of  wheat  on  7  acres. 
What  was  the  average  yield  per  acre  ? 

38.  At  $363  for  9  chests  of  tea,  how  much  will  1  chest 

cost? 

How  much  is 


39.  $  of  89  rods  ? 

40.  |  of  182  pounds  ? 

41.  TV  of  166  bu.  ? 


42.  &  of  630  gal.  ? 

43.  \  of  365  da.  ? 

44.  of  752  ? 


45.  How  much  is  1  seventh  of  $42  ?     How  much  are  6 

sevenths  of  $42  ? 
40.  A  laborer  who  earns  $42  a  month,  pays  |  of  his 

earnings  for  his  board  and  washing.     How  much  do 

his  board  and  washing  cost  him  ? 
10 


122  FRACTIONS. 

47.  The  cleared  land  on  a  farm  of  80  acres  is  T70  of  the 
whole  farm.    How  many  acres  are  clear 

48.  Last  year  a  dairy-man  made  77  cheeses,  and  this 
\  ar  he  has  made  jf  as  many.    How  many  cheeses 
IMS  h  •  made  this  year  ': 

;  '.   I'  ii  school  are  40  pupils,  ?  of  whom  study 

grammar.    How  many  study  grammar  ? 

50.  A  lumber  dralrr  has  ^:>0  thousand  feet  of  lun, 
of  which  is  pine.  How  many  feet  of  pine  lu 
bathe? 

••"/.  In  a  shoe-store  there  are  12  doz.  pairs  of  m 

and  J  of  them  are  ladies'  sizes.    How  many  pairs  of 
ladies'  rubbers  are  there  in  the  stoi 

I  indf90  of  $100. 

How  much  is 

53.  |of!26gnl.  ?  55.  $  off  of  182? 

54>  Aof  I  of  126  gal.?  66.  f  of}  of  182? 

<;.  llo\\-  iniu-h  will  I  Ib.  of  cinnamon  cost,  at  $.GO  a 
pound  'J.      VtOMUt  ,"../'  179. 

68.  A  tinsmiih  used  $  of  3  sheets  of  tin,  in  making  a 
pail.    How  much  tin  did  he  use? 

69.  How  much  is  j  of  9  feet  ? 

010.  When  coal  is  $8  a  ton,  how  much  does  |  of  a  ton 
cost? 

IIow  much  is 


S   of  5  sq.  yd.  ? 
62.   |  of  4  quires  ? 


63.  -&  of  63  gal.  ? 

64.  A  of  13:> 


30.    An  Integer  by  a  Mixed  Number. 

65.  At  $.10  a  pound  for  sal  soda,  how  much  will  2  Ih 
cost  ?    How  much  will  A  Ib.  cost  ?    How  much  will 
2J  Ib.  cost  ? 

66.  In  a  pasture  are  15  cows,  and  4 1   tinii-s  as  many 
sluvp.     How  many  sheep  are  in  tho  pasture? 


MULTIPLICATION.  123 

67.  One  family  burned  12  thousand  feet  of  gas  in  a 
year,  and  another  burned  3£  times  as  much.    How 
many  thousand  feet  did  the  second  family  burn  ? 

68.  How  many  miles  will  a  railroad  train  run  in  2]  h., 
at  the  rate  of  24  mi.  an  hour  ?    Methods,  page  179. 

69.  How  much  will  3$  gross  of  wood  screws  cost,  at  $.64 
per  gross  ? 

70.  One  year  I  raised  18  bu.  of  turnips,  and  4f  times  as 
many  potatoes.    How  many  bushels  of  potatoes  did 
I  raise  ? 

71.  A  family,  in  one  year,  use  20  Ib.  of  coffee,  and  S/^ 
times  as  much  sugar.    How  much  sugar  do  they  use  ? 

How  much  are 


72.  3|  times  5  yd.  ? 

73.  12£  times  8  da.  ? 

74.  15£  times  9  ? 


75.  6f  times  8  gal.  ? 

76.  6f  times  5  mi.  ? 

77.  24|  times  8  ? 


3J     A  Fraction  or  a  mixed  Number  by  a  Fraction  or  a 
IVXixed  Number. 

78.  Grace  used  1  half  of  f  of  a  roll  of  wall  paper,  in 
papering  a  box.  What  fraction  of  a  roll  did  she  use  ? 

70.  When  a  bushel  of  com  is  worth  $|,  how  much  will 
1  fourth  of  a  bushel  cost  ?  How  much  will  3  fourths 
of  a  bushel  cost  ? 

80.  How  much  will  -J  gal.  of  molasses  cost,  at  $|  per 

gallon  ?      Methods,  page  179. 

81.  If  I  feed  my  chickens  f  of  f  of  a  bushel  of  grain  in 
a  week,  what  part  of  a  bushel  do  I  feed  them  ? 

82.  A  man  who  owned  £i  of  a  schooner,  sold  |  of  his 
share.    What  part  of  the  schooner  did  he  sell  ? 

What  fraction  is  equal  to 


83.  f  Of  ft  of  ft  rod  I 

84.  |  of  -&V  of  a  cargo  of  tea  ? 


85.  f  of  |f  ? 

86.  |  of  -f  of  f  i  ? 


U'i  FRACTIONS. 

.   Lust  year  my  trees  bore  2^  bushels  (or  J  bushels)  of 
plums,  and  I  sold  J  of  them.     How  numy  bushels 

aid  i  s-ii  :- 

88.  At  $1 1  a  pound,  how  much  will  I  Ib.  of  tea  cost  ? 
£0.  How  much  is  J  of  Is? 

H'-w  much  is 

00.  i  of  15f  t  ftf.  ^f  of  6f  ? 

;of4*tt  PA  ^  of  0^? 

0£  t&  is  how  many  tw«  in  .  thsof  ft  dollar?     How  i 
is  \  of  $^0  ?    Then,  how  much  is  }  of  $J  ? 
!Io\\-  niudi  is  |  of  $J  ?    How  much  is  J  of  * 

96.  How  much  is  J  of  |  yd.  ? 

'',.    How  much  is   ?  Of  J  yd.  ?      Method*,  page   I 

^5.  How  much  will  J  Ib.  of  shot  cost,  at  $,30  a  pound  ? 
' '.  If  a  boy  saws  |  of  a  cord  of  wood  in  a  day,  how 
much  can  ho  saw  in  J  of  a  day  ? 

100.  A  family  burns  3  of  a  gallon  of  kerosene  in  a  week. 
How  much  do  thy  burn  in  f  of  a  week  ? 

101.  In  the  last  problem,  how  may  the  numerator  0  of  the 
result  be  obtained  ?    How  may  the  denominator  'J  i 
obtained? 

102.  When  the  factors  are  fraction*,  June  may  their  product  "be 
obtained  f 


How  much  is 
10S.       of  *  mi.  i 


104.  -,V  of  f  da.  ? 


What  is  the  product  of 

107.  ^timef  of  a  ton  t 

108.  |  multiplied  by  ^  ? 


105.  |  of  $|  ? 
10G.  if  of  }  T.  ? 

111.  At  $  j  a  yard,  how  much  must  I  pay  for  2J  yards 
(or  V  yards)  of  linen  ? 

V  farmer,  in  seeding  8|  acres  of  land,  usc-d  I  of  a 
bushel  of  clover  sei-d  to  the  acre.  How  much 
clover  seed  did  he  use  ? 


DIVISION.  125 

113.  The  sulphur  and  saltpeter  in  a  pound  of  gun- 
powder weigh  -fs  of  a  pound,  and  the  charcoal 
weighs  3  J  times  as  much.  What  is  the  weight  of 
the  charcoal  ? 

114-  A  young  man  bought  2]  yd.  of  broadcloth  for  a 
coat,  at  $5i  a  yard.  How  much  did  the  coat  pat- 
tern cost  ? 

115.  How  much  will  8J  cd.  of  wood  cost,  at  $6|  per  cord  ? 

116.  A  boy  husked  7J  bu.  of  com  in  a  day,  and  his 
father  husked  3]   times  as  much.      How  many 
bushels  did  the  father  husk  ? 

117.  A  merchant  having  10.]  yd.  of  serge,  sold  ?  of  it,  at 
$1T'0  a  yard.    How  much  did  he  receive  for  it  ? 

What  is  the  result  in  each  of  the  next  eight  problems  ? 


118.  *  of  $2f  ? 

119.  |  x  64|? 

120.  f  of  7|  bar.  ? 

121.  13}doz.  x  £ 


122.  \  mi.  x  4f  ? 

123.  2%  x  f  yd.  ? 

124.  $x  fVof  Gf  lb. 
J25.  2£  x  Cf  x  8|  ? 


SECTION    VI. 

3)  lYIS  ION. 
32.   A  Fraction  by  an  Znteger. 

1.  IF  I  divide  |  of  a  melon  equally  between  two  girls, 
what  part  of  the  §  of  a  melon  will  each  girl  have  ? 

2.  How  much  is  1  half  of  §  of  a  melon  ? 

3.  What  is  the  quotient  of  f  divided  by  2  ? 

4.  Multiplying  by  £  obtains  the  same  result  as  dividing  by 
what  number  ?     Multiplying  by  \ :  ?     By  £  ? 

<£.  If  3  oranges  are  worth  T90  of  a  pine-apple,  what  part 

of  a  pine-apple  is  1  orange  worth  ? 
6.  If  8  yd.  of  shirting  cost  $|i,  how  much  will  1  yd.  cost  ? 


12G  FRACTIONS. 


much  i.i  What  i<  the  quotient  of 

"ne  half  off  ?  11.  $ 

8.  One  ninth  of  ff  ?  12.  ff  divid.-d  by  9? 

9.  One  sixth  of  f  \  ?  IS.  $ff  divided  by  $6  ? 
10.  One  fifth  of  ff  ?  14.  ff  Ib.  di\  i  lb.  f 

What  effect  it  produced  by  dividing  the  numerator  of  a  frac- 
tion by  an  integer  f     Why  f 
Divide  ff  by  9.     Divide  the  same  fraction  by  6. 
77*  iff  are  uow  many  times  4  ?    How  many  times  8  ? 

18.  A  boy  sold  6  quarts  of  beechnuts  for  $Jf.    How 
much  did  he  rec  quart  for  them  ? 

10.  If  J5  of  a  barrel  of  flour  will  last  12  persons  1  week, 
how  much  Hour  will  last  1  person  the  sam< 

20.  I  cut  \  of  a  melon  into  2  equal  pieces.    AYh; 

of  the  melon  was  each 
.'/.   H.»w  iniu-li  is  1  half  of  ^  of  a  melon? 

.'.'.  If  I  pay  $|  (or  $fj)  for  4  pounds  of  sugar,  how 
much  is  the  sugar  per  pound  ? 

.A  :•  feeds  2  horses  5  of  a  bushel  of  oats  daily. 

1 1  <  >w  many  oats  does  he  feed  each  horse  ? 


IIow  many  times  are 
24.  I  contained  in  f  ? 

in  f  ? 

26.  8  contained  in     ? 


How  much  is 

27.  One  third  of  |? 

28.  One  fifth  off? 

29.  One  eighth  of  | 


50.  What  tffect  it  produced  by  multiplying  the  denominator  of  a 
fraction  by  an  integer  f     Why  f 

51.  A  fruit-dealer  sold  10  muskmelons  for  $J.    How 
much  did  IK  apiece  for  them? 

>hanna  picked  J  of  a  bushel  of  strawK-rru-s  in  4 
hours.    IIow  many  berries  did  she  pick  in  an  hour? 
S3.  Find  the  quotient  of  f  divided  by  0.     Of  |  divided  by  5. 
$4.  |$f  is  12  times  what  number  ? 


DIVISION.  127 

33.  A  Mixed  Number  by  an  Integer. 

85.  If  li  apples  are  divided  equally  between  2  boys,  how 
many  thirds  of  an  apple  will  each  boy  receive  ? 

36.  If  7  bushels  of  oats  cost  $2|,  what  is  the  price  per 
bushel  ? 

87.  A  man  mowed  41-  acres  of  grass  in  3  days.    How 
much  did  he  mow  in  1  day  ? 

88.  When  photographs  cost  $2}2  per  dozen,  how  much 
are  they  apiece  ? 

80.  When  eggs  are  $.37£  per  doz.,  what  is  1  egg  worth  ? 

40.  A  butter  buyer  paid  $84?  for  9  tubs  of  butter.    How 
much  did  he  pay  for  1  tub  ? 

How  many  times  are 

41.  $6  contained  in  $41$  ? 

42.  8  h.  contained  in  16f  h.  ?  46.  |  of  16£  h.  ? 


How  much  is 


45. 


47.  $  of  23£  yd.  ? 

48.  of  54    bu. 


43.  5  yd.  contained  in  28£  yd.  ? 

44.  45  bu.  contained  in  54£bu.? 

40.  How  many  weeks  will  35|  pounds  of  butter  last  a 
family  that  use  4  pounds  per  week  ? 

50.  If  3  ,'j  bar.  of  flour  last  49  persons  1  month,  what 
part  of  a  barrel  will  last  1  person  the  same  time  ? 

34.  An  Integer  by  a  Fraction. 

51.  If  each  person  at  dinner  receives  J  of  a  pie,  and  a 
whole  pie  is  eaten,  how  many  persons  dine  ? 

62.  Among  how  many  children  can  a  melon  be  divided, 
if  each  child  receive  -^  of  a  melon  ? 

53.  At  $\  apiece,  how  many  market-baskets  can  be 
bought  for  $2  ?     How  many  for  $3  ?     For  $5  ? 

54.  How  many  bushels  of  lime  can  be  bought  for  $4,  at 
$|  a  bushel  ? 

55.  How  many  bushels  can  be  bought  for  $4,  at  $|  a 

bushel  ?       Methods,  page  ISO. 


128  FRACTIONS. 

56.  Into  how  many  pieces,  each  §  yd.  long,  can  0  yd.  of 

wire  1»"  cut  ?  O 
.<;.   How  many  days  will  i»  Imshcls  of  oats  last  a  horse, 

if  he  eats  j  of  a  bushel  daily  ? 

68.  A  merchant  paid  $30  for  a  piece  of  linen,  at  $T80  per 
How  many  yards  were  there  in  i 


I  low  many  tinu-s  a: 
59.  f  gal.  contained  in  7 
CO.  |  yd.  contained  in  16  yd.yf 
67.   »  wk.contaiiu-d  in  1:2  wkf? 


What  is  the-  quotk-nt  of 

.     ;:i!.   divided  |,y  *?    ' 

63.  16yd.  divi.h  .1  by  I?' 

.'  wk.  dividrdbyf? 


35.  An  Integer  by  a  Mixed  Number. 

.  How  many  neck-ties,  each  1 J  yd.  (or  J 
be  made  from  a  piece  of  ribbon  containing  1(> } 

66.  A  iiKTrhunt   tailor  made  30  yd.  of  cussimere  i 
suits  of  clothes,  using  7J  yd.  of  cloth  for  « 
llow  many  suits  did  he  mak< 

67.  A  grocer  paid  $18  for  mackerel,  at  $1  j  a  kit     How 
many  kits  did  lu-  I  my  ?  f /) 

68.  At  $2|  a  bushel,  how  many  bushels  of  grass  seed 
can  be  bought  for  $20 ? 

69.  How  many  yards  of  cloth  can  be  mu<l<   fr-mi  <l^  Ib. 
of  wool,  allowing  lj  11 ».  to  the  yard?  $7 fa  ~ 

70.  A  bricklayer  received  $72  for  lal».>r.  at  $2^  j>cr  day, 
How  many  days  did  he  work  ?^  > 

71.  How  many  times  arc  2|  contained  in  13  ? 

78 .  80  -~  2f  =  how  many  ?     |     73.  625  -s-  6J  =  how  many  ? 

36.  Fractional  Part  or  Parts  given,  to  find  tho  Whole. 

1 1*  \  bar.  of  flour  costs  $2,  how  much  will  1  bar.  c 

It'  '.  of  a  Imshel  of  potatoes  will  last  a  family  5  days* 

how  many  days  will  a  bushel  last  tl. 
76.  If  i  quire  of  paper  costs  $.12J,  how  much  will  a 

quire  cost  ? 


DIVISION.  129 

77.  If  a  farmer  can  hoe  -1  of  an  acre  of  corn  in  8  hours, 
how  many  hours  will  it  take  him  to  hoe  an  acre  ? 

78.  If  i  of  a  ton  of  old  iron  is  worth  $4J,  hew  much  is 
a  ton  worth  ? 

79.  I  of  my  kite  string  is  7j  yd.  long.    What  is  the 
length  of  my  kite  string  ? 

80.  Reuben  gave  $vv30  for  bananas,  spending  -]•  of  all  his 
money.     How  much  money  had  he  ? 

81.  One  day  a  hunter  used  -J  Ib.  of  shot,  which  was  4  of  ^ 
all  he  had.     How  many  pounds  of  shot  had  he  ? 

82.  12  is  |  of  how  many  ?       i  86.  •&  is  \-  of  what  number  ? 

83.  36  is  |  of  how  many  ?//  '\  87.  3^  is  %  of  what  number  ?  «  /  ' 
8J>.  T^  is  \  of  what  numluT  ?   '  «s',s'.  17j-  is  ?.  of  what  number  ? 
85.  \%  is  |  of  what  number  V  f  59.  9£  is  |  of  what  number  ? 


.•• 


P0.  If  |  of  a  cord  of  wood  costs  $6,  how  much  does 

of  a  cord  cost  ? 
91.  If  i  of  a  pound  of  raisins  cost  $.16,  how  much  will 

J  of  a  pound  cost  ?    How  much  will  a  pound  cost  ? 

03.  If  a  man  can  cut  ~  of  a  cord  of  wood  in  4  hours, 
how  many  hours  will  it  take  him  to  cut  1  cord  ? 

93.  When  -5  bar.  of  flour  are  worth  $6,  what  is  the  price 
per  barrel  ? 

94.  A  mechanic  worked  f  of  a  week,  and  received  $10. 
How  much  were  his  weekly  wages  ? 

95.  A  fruit-grower,  after  selling  9  bushels  of  plums, 
found  he  had  \  of  his  plums  left.      How  many 
plums  did  he  raise  ? 


96.  8  is  f  of  what  number  ? 

97.  6  is  |  of  what  number  ? 

98.  10  is  f  of  what  number  ?  /* 

99.  12  is     of  what  number  ? 


100.  22  is  |  of  what  number  ? 

101.  35  is  f  of  what  number  ?    j 

102.  125  is  |f  of  what  number? 

103.  150  is  T«L  of  what  number  ? 


130  FRACTIONS. 

37.    A  Fraction  or  a  Wlixcd  Number  by  a  Traction* 

A  blacksmith  received  J  of  a  dollar  for  s 
horse-shoes,  at  J   of  a  dollar  each.     How  many 
shoes  did  he  set  ? 

105.  If  I  of  a  yard  of  velvet  ribbon  will  cover  In 
book,  how  many  needle-books  will  .*  of  a  yard  co 
1  low  many  books  will  lj  yards  (or  V  jd«)>  °°Tt 

106.  Some  soldiers  who  messed  toj:  ed  6| 
pounds  of  meat  daily.    How  many  soldiers  v. 
there,  there  being  J  of  a  pound  of  in.  at  in  a 

107.  A  ship's  crew  have  9J  barrels  of  biscuit    How 
many  weeks  will  it  last  them,  if  they  use  f  of  a 
barrel  weekly  ? 

108.  When  dividend  and  dicuor  an  nmilar  fraction*,  how  u  the 
ditition  performed  t 

What  is  the  quotient  of 
100.  |  yd.  divided  by  f  ?         I  113.  5f  divided  by  f  ? 

110.  ffc  mi,  divided  by  ^?        llf.  6f  Ib.  divided  by  f  Ib.  ? 

111.  Wf  divided  by  ^  ?        115.  5f  Ib.  divi.kd  by  \  II).  ? 
11*.  16|  divi.K-.l  by  |  ?  |  116.  4|  wk.  ,livick-.l  by  f  wk.  ? 

^ome  men  bought  J  of  a  steam-boat,  each  man 
huyini:  ^  of  her.     How  many  men  wcr 
118.  How  much  kerosene  can  be  bought  for  tfa  at  $] 

Ballon  ?      Method*,  page  ISO. 

\  i'armer  sold  some  corn  at  $J  a  busli.-l.  and  re- 

ifed  ^7|  for  it     How  many  bushels  did  he  • 
.   How  many  days  will  6J  pounds  of  butter  last  a 

family,  that  use  J  of  a  pound  a  day  ? 
121.  Halbert  skated  1CJ  miles,  at  the  rate  of  758  of  a 
mile  in  a  minute.     How  many  minutes  did  it  take 
him! 


How  many  times  are 
12*.   |  contained  in  J  ? 

123.  -fy  contained  in  4$  1 

124.  \  contained  in   J  ? 


Divide 

1S5.   A  T.  by  |  T. 
126.  5Vy  Ib.  by  |  Ib. 
le^ft.  by  {ft. 


DIVISION.  131 

128.  How  many  quires  of  note  paper  can  I  buy  for  f  of 
a  dollar,  at  i  of  a  dollar  per  quire  ? 

129.  If  a  family  use  J  of  a  barrel  of  potatoes  in  a  week, 
how  many  weeks  will  §  of  a  barrel  last  them  ? 

130.  At  $  j  a  pound,  how  many  pounds  of  coffee  can  be 
bought  for  $T90  ? 


How  many  times  is 

131.  |  contained  in  |  ? 

132.  \  contained  in  ^  ? 

133.  contained  in      ? 


What  is  the  quotient  of 
134.  2f-  wk.  divided  by  £  wk.  ? 
J35.  5|  mi.  divided  by  TV  mi.  ? 
156.  3£  mi.  divided  by  $  mi.  ? 


137.  How  many  pounds  of  citron  can  be  bought  for  $|, 
at  $|  per  pound  ? 

138.  Nellie  paid  out  $£  for  candies,  at  $?-  a  pound. 
How  many  pounds  of  candies  did  she  buy  ? 

130.  If  a  farm  hand  can  plant  430  of  a  field  in  one  clay, 
how  many  days  will  it  take  him  to  plant  f  of  it  ? 

140.  A  grocer  exchanged  cheese  for  honey,  at  the  rate 
of  1  Ib.  of  cheese  for  f  of  honey.     How  many 
pounds  of  cheese  did  he  give  for  4J  Ib.  of  honey  ? 

141.  If  dividend  and  divisor  are  dissimilar  fractions,  wTiat  step 
is  necessary,  preparatory  to  performing  the  division  ? 

142.  Then,  when  can  a  mixed  number  or  a  fraction  le  divided  ty 
a  fraction? 

143.  When  dividend  and  divisor  are  dissimilar  fractions,  how  is 
the  division  performed  f 

144-  How  many  milk-cans  can  be  made  from  12 f  boxes 
of  tin,  if  it  takes  |  of  a  box  for  one  can  ? 


145.  £    is  how  many  times  f  ? 

146.  \^  are  how  many  times  f  ? 

147.  %\  are  how  many  times  -fa  ? 


148.  Divide  2£  by  f 

149.  Divide  7-J-  by  f 

150.  Divide  4£  by  f . 


151.  My  garden,  which  con  tans  |  of  an  acre,  is  |  of  my 
whole  village  lot.    What  is  the  size  of  my  lot  ? 


FB  ACTIONS. 

I-''.  In  January  I  used   t\  of  a  ton  of  coal,  which  was 
T25  of  my  year's  supply.    How  much  was  my 
supply  ? 

•  Jasper  is  18}  years  old.  and  his  age  is  equal 
of  his  father's  age.    How  old  is  his  fat! 
V  man's  family  expenses,  which  are  $12}  a 
are  J  of  what  he  earns.    What  are  his  earnings  ? 
I  gave  J  as  much  for  my  wagon  as  for  my  horse, 
and  my  wagon  cost  me  $96}.     How  much  did  my 
horse  cost  me  ? 


\  is  |  of  what  number  ? 
}  J  is  |  of  what  number  ? 

158.  ft  is  J  of  what  number  ? 

159.  -fj'is-fyof  what  numltcr  ? 

160.  ~fa  is  j  |  of  what  number  ? 


161.  3}  is  4  of  what  number? 

162.  5f  is  |  of  what  nut: 

163.  4f  is  f  of  what  nun. 

164.  7|  is  Vft  of  what  number! 
1 8}  is  |  of  what  number  ? 


38.  A  Fraction  or  a  lYIixod  Number  by  a  Zttixod  Number. 

.  I  low  many  days  will  11  j  lb.  of  meat  last  a  family 
that  EUKfl  Ij  lb.  daily?    Jf*t*w«,  |>»  /    t*t, 

I  I«»w  many  j.  ws-liarj-s  can  be  bought  for  $.18J,  at 
$.06 j  apiece? 

168.  At  $61  a  pair,  how  many  pairs  of  boots  can  be 
bought  for  *! 

169.  A  boy  can  nil  res  of  hay  in  a  day.     How 
long  will  it  take  him  to  rake  J  of  an  a< 

170.  How  much  clover  seed  can  be  bought  for  $|,  at 
$3|  a  bushel  ? 

11 1.  When  cranberries  are  $9J  a  barrel,  what  part  of  a 
barrel  can  be  bought  for  * 


What  is  the  quotient  of 
17S.   I  divided  by  2J  ? 
175.   f  divided  by  3}  ? 
6|  divided  by  lOf? 


How  many  timc^  are 

175.  \\  contained  in   5f  ? 

176.  3J  contained  in 
•:    contained  in 


DIVISION.  133 

178.  A  carman  drew  1343  T.  of  freight,  taking  1|  T.  at  a 
load.     How  many  loads  did  he  draw  ? 

179.  A  wood  sawyer  sawed  and  split  12  \  cd.  of  wood  in 
6  J  days.    How  many  cords  did  he  average  per  day  ? 

180.  If  3  J  bu.  of  wheat  cost  $4?,  how  much  will  1  bu. 
cost? 

181.  How  many  hours  will  it  take  a  canal-boat  to  run 
21 1  miles,  at  the  average  rate  of  2^  miles  an  hour  ? 

182.  What  part  of  a  barrel  of  sweet-potatoes  can  be 
bought  for  $3J,  at  $6|  a  barrel  ? 


How  many  times  arc 

183.  2f  contained  in  5$  ? 

184.  If  contained  in  4/ff 

185.  S1   contained  in  8 


What  part 
186.  Of  $8£  are 
157.  Of  10£  ft.  are  2^  ft.  ? 
188.  Of  4TV  h.  are  If  h.  ? 


159.   TFfon  the  divisor  is  a  mixed  number,  what  step  is  necessary, 
'before  performing  the  division  f 

190.  Then,  how  is  a  mixed  number  or  a  fraction  divided  ty  a 
mixed  number  f 

191.  A  farmer  cut  7J  T.  of  hay  from  a  meadow,  that 
yielded  1§  T.  to  the  acre.    How  many  acres  were 
there  in  the  meadow  ? 

A  hop  grower  picked  6|  T.  of  hops,  from  a  yard 
which  averaged  1£  T.  to  the  acre.     How  many 
acres  were  there  in  the  hop-yard  ? 
103.  What  part  of  a  basket  of  peaches  can  be  bought  for 
$11,  at  $31  per  basket? 


How  many  times  are 
104.  $1|  contained  in 
195.  2  J  yd.  contained  in  5f  yd.? 


What  is  the  quotient  of 

196.  $1|  divided  by  $12£  ? 

197.  2£  yd.  divided  by  5f  yd.? 


134  I'll  ACTIONS. 

SECTION  VII 


1.  Reduce  ff,  4f  J,  and  fff  to  their  lowest  terms. 

2.  Reduce  {,  f  ,  and  j  to  similar  fractions. 

S.  What  is  tin-  ronunoM  .It-nominator  of  the  least  similar 
fractions  to  which  fifths,  eighths,  and  tenths  can  be  re- 
•  luced? 

4.  A  grocer  has  T*2  bar.  of  A  sugar,  ]  J  bar.  of  B  sugar, 
and  TVo  bar.  of  yellow  sugar.    Of  what  kind  of  ^ugar 
lias  he  the  most  ? 

5.  How  many  yards  of  Marseilles  goods  will  be  required 
for  3  doz.  Tests,  allowing  }  yd.  to  a  Test? 

G.  Kate  bought  10  yards  of  Scotch  gingham,  at  * 

y:ml.     How  much  did  it  cost  her  ? 
.   In  a  certain  Tillage  th«-n.-  are  497  dwelling  houses, 
ami    i    of  them   aiv    <>f   1-rick.       How   many   1  trick 
houses  arc  there  in  the  Tillage  ? 

8.  How  many  days  are  f  of  a  common  year  ? 

9.  How  much  arc  the  daily  wages  of  a  factory  girl,  who 

ek  ? 

JO.  A  young  lady  paid  $5  for  1  doz.  handkor. 

What  part  of  a  dollar  did  each  handkerchief  cost? 
11.  At  $4  for  5  ducks,  how  much  will  1  duck  cost  ? 

/  .'.  1  low  many  hours  must  a  boy  work  to  earn  $.; 
$.10  an  hour  ? 

How  much  is 

13.  \  of  92  dozen  ?  16.  |  of  ! 

14.  H  of  $32  ?  17.  Jh  of  925  ? 
1  •'-  iV  of  H  of  a  box  of  soap  ?              18.  &  of  ft  ? 

19.  One  week  a  factory  operative  made  only  -fa  of  full 
time.    How  many  days  did  he  work  ? 


REVIEW     PROBLEMS.  135 

20.  A  lady  having  -}5  of  a  pound  of  worsted,  used  f  of 
it  in  making  a  lamp  mat.    What  part  of  a  pound 
did  she  use  ? 

21.  I  bought  %  of  a  piece  of  carpeting  which  contained 
61:j    yards,  for  a  carpet.      How  many  yards  were 
there  in  the  carpet  ? 

22.  A  hardware  dealer  sold  a  keg  of  nails  for  $5370,  and 
his  gain  was  $~.  How  much  did  the  nails  cost  him? 

23.  If  I  have  $7n90,  how  much  must  I  earn  to  have  $10  ? 

24.  If  a  farm  hand  earns  $9  in  £§  of  a  month,  what  are 
his  monthly  wages? 

25.  If  4  yards  of  silicia  costs  $!J,  how  much  will  3  yards 
cost? 

26.  10  is  |  of  some  number ;  how  much  is  |  of  the  number  ? 

27.  12  is  £  of  some  number  ;  how  much  is  f  of  the  number  ? 

28.  20  is  |  of  some  number ;  how  much  is  ^  of  the  number  ? 

29.  How  much  is  -^  of  the  number  of  which  120  is  |f  ? 

30.  How  much  is  -^  of  the  number  of  which  144  is  T97  ? 

31.  If  5  bushels  of  wheat  cost  f  of  $10,  what  will  be  the 
cost  of  6  bushels  ? 

32.  If  a  barrel  of  flour  is  worth  12  times  as  much  as  a 
bushel  of  oats,  and  flour  is  $8|  a  barrel,  how  much 
are  oats  a  bushel  ? 

33.  A  driver  paid  $287^  for  two  yoke  of  oxen.    How 
much  did  he  pay  for  1  ox  ? 

34.  If  a  man's  wages  are  $9  a  week,  in  how  many  weeks 
will  he  earn  $33|  ? 

35.  If  two  boxes  of  lemons  cost  $5J,  how  many  boxes 
can  be  bought  for  $16§  ? 

36.  A  drover,  by  selling  a  lot  of  sheep  for  $25  above 
cost,  gained  \  of  their  cost.     For  how  much  did  he 
sell  the  sheep  ? 


FBACTIONS. 

•  /;.  My  harness  cost  $31  j.  which  was  *  as  much  I 

cost  of  mj  cutter.     What  was  the  cost  of  both  ? 

38.  A  mason  used  12  J  bu.  of  sand  in  making  a  bat 
mortar,  using  Ijj  bu.  of  sand  to  1  bu.  of  lime.    How, 
many  bushels  of  lime  did  he  use! 

39.  }  of  12  are  how  many  times  3  ? 

40.  f  of  27  are  what  part  of  54? 

41.  f  of  27  are  3  times  what  number? 

42.  |  of  27  arc  )  of  what  number  ? 

43.  }  of  27  are  f  of  what  number  ? 

44.  48  arc  |  of  what  number  ? 

45.  A  man  paid  $3}  for  a  satin  vest  pan  ing  at 
the  rate  of  $8j  a  yard.     What  was  the  length  of  the 
Test  pattern  ? 

10  pound  out  |  gal.  of  win-  from  a  gallon 
jug  that  was  j  full  How  much  wine  was  tin -n  left 
in  the  jug? 

47.  I  bought  3  T.  of  coal,  and  used  j  T.  one  month  and 
T90  T.  the  next  month.     How  much  coal  had  I  1 

48.  A,  B,  and  C  together  own  a  woolen  factory.    A  owns 
§  of  it,  and  B  J  of  it     What  part  of  it  does  C  own  ? 

49.  A  man   travrlrd  14  J  mi.  by  railroad,  64£  mi.  by 
steamboat,  and   far  enough   by  stage  to  mak 
whole  journey  108 F93  mi.    How  far  did  he  travel  by 
stage? 

•  <".  What  number  must  be  added  to  the  sum  of  $  and 

6J  to  make  103? 

51.  From  the  sum  of  |,  f ,  |,  and  $,  subtract  If. 

52.  From  16}  subtract  the  sum  off,  |,  and  lOf. 

53.  1  +  5£  are  how  much  less  than  10  +  4|  ? 

54.  What  is  the  difference  between  J  +  i  and  |  +  |l 

55.  12  times  fj  are  J  of  what  number? 

56.  |  of  10  times  |f  are  -^  of  what  number? 


KEVIEW    PROBLEMS.  137 

57.  How  many  yards  of  silk  will  a  tailor  use  in  facing  9 

coats  if  he  uses  A?  of  a  yard  for  each  ? 
55.   |  of  12  are  $  of  what  number? 

59.  \  of  15  are  $  of  what  number  ? 

60.  f  of  24  are  f  of  what  number  ? 

61.  £  of  48  are  ^  of  what  number  ? 

62.  |  of  30  are  £  of  what  number  ? 

63.  How  many  hours  must  a  boy  work  to  earn  $J  if  he 
earns  $530  an  hour? 

64.  At  $12  a  ton,  how  much  will  f  T.  of  hay  cost  ? 

65.  If  the  materials  for  7  gal.  of  wine  cost  $4,  how  much 
will  they  cost  for  4  gal.  ? 

66.  If  a  man  can  saw  and  split  6  cd.  of  wood  in  4  da., 
how  long  will  it  take  him  to  saw  and  split  9  cd.  ? 

67.  How  much  will  8|  Ib.  of  candy  cost  at  $f  a  pound  ? 

68.  What  will  be  the  cost  of  12f  yd.  of  carpeting,  at 
$1 1  a  yard? 

69.  James  hoed  a  piece  of  corn  in  5§  da.,  hoeing  f  A. 
each  day.    How  many  acres  were  there  in  the  piece  ? 

70.  Farmer  F.  has  25  cows,  and  his  neighbor  G.  has  5 
less  than  f  as  many.     How  many  cows  have  both  ? 

71.  If  a  boy  can  pump  4£  gal.  of  water  in  1  minute, 
how  many  minutes  will  it  take  him  to  fill  a  tank 
which  holds  155  gal.? 

72.  At  $lf  a  basket,  how  many  baskets  of  tomatoes  can 

be  bought  for  $9 ^  ? 

73.  48  is  $  of  how  many  times  10  ? 

74.  |  of  64  are  |  of  how  many  times  12  ? 

75.  |  of  64  are  |  of  how  many  times  £  of  24  ? 

76.  |  of  64  are  4  times  what  part  of  50  ? 

11 


—>,/*- 

**«-««"% 

CHAPTER   YI.       &« 

~~~~~~£i** 


CONVERSE    OPERATIONS. 


SWBTXACTJ 


1.  THE  parts  of  a  farm  arc  35  acres  of  tilled  land,  1  7 
acres  of  meadow,  25  acres  of  pastun  \  and  '^  acres 
of  woodland.  IIow  many  acres  are  tin-re  in  tin- 
farm  ? 

A  kin  /       K     per  in  Chicago  has  35  carriages, 

Hi  of  which  an-  douMe  rama^s.     How  in;:. 
carriages  has  h«-  't 

3.  Two  pieces  of  cloth  nu  'usniv  :>",  yd.  1  «jr.,  and  one 
of  them  is  8  yd.  3  qr.  long.  What  is  the  l-n^h  of 
the  otli 

..    A  woman  wrht  to  a  t«-;i  store  with  $'-2.1'>.     Sh«-  paid 
$.75  for  6  pounds  of  sugar,  $.40  for  2  pounds  of 
coffee,  and  the  balance  of  her  money  for  a  poun 
tea.     IIow  much  was  the  t«-a  a  pound  ? 

5.  A  miller  had  269  bushels  of  wheat,  but  aft*  r  grind- 
ing a  part  of  it  into  flour.  In-  liiuls  he  has  87  bushels 
remaining.  How  many  buslu-ls  has  he  ground  ? 

<?.  A  Vermont  farm-  r.  liter  Belling  806  sheep,  hju 
n-maining.     How  many  ifliirp  liad  he  at  lir 


MULTIPLICATION    AND    DIVISION.       139 

7.  Joel  is  5  ft.  2  in.  high,  and  Jasper  is  3  ft.  11  in.  high. 
What  is  the  difference  in  their  heights  ? 

8.  What  is  the  sum  of  2A  da.,  5f  da.,  9^  da.,  and  |  da.  ? 

Addition  is  putting  parts  together  to  form  a  whole,  and  sub- 
traction is  taking  away  a  part  or  parts  from  the  whole.  Hence, 
addition  is  the  reverse  of  subtraction. 

Conrcrsc  Operations  are  those  arithmetical  processes 
which  are  the  reverse  of  each  other. 

9.  The  parts  of  a  number  are  15,  92,  and  43.     What  is  the 
number  ? 

10.  The  sum  of  two  numbers  is  18  gal.  2  qt.,  and  one  of  them 
is  4  gal.  3  qt.  1  pt.     What  is  the  other  ? 

11.  The  sum  of  three  numbers  is  37£ ;  one  of  them  is  18|,  and 
another  is  12£.    What  is  the  other  number  ? 

12.  The  minuend  is  94,  and  the  subtrahend  is  48.     What  is 
the  difference  ? 

13.  The  minuend  is  3$,  and  the  remainder  is  2f.    What  is  the 
subtrahend  ? 

Ut.  The  subtrahend  is  10  11).  4  oz.,  and  the  remainder  is  5  Ib. 
C  oz.     What  is  the  minuend  ? 

15.  What  is  the  difference  between  i|  wk.,  and  -J-fJ.  wk.  ? 

16.  The  greater  of  two  numbers  is  $3.15,  and  the  less  is  $1.27£. 
What  is  their  difference  ? 

17.  The  greater  of  two  numbers  is  $3/ff,  and  their  difference 
is  $1|.     What  is  the  less  number  ? 

IS.  The  less  of  two  numbers  is  $1.27£,  and  their  difference  is 
$1.87£.     What  is  the  greater  number  ?  (Sec  Manual,  Pago  173.) 


SECTION    II. 

MVZ.TITZICd.TIOJV  dLJV®    DITISIOJV. 

1.  How  many  square  rods  arc  there  in  a  field  35^  rd. 
long  and  9  rd.  wide  ? 

2.  In  finding  the  cost  of  30  barrels  of  apples,  at  $2.12A 
per  barrel,  which  number  is  the  multiplicand,  which 
is  the  multiplier,  and  which  is  the  product  ? 


140  CONViiKSi;    OP1EJLTI01 

3.  A  grocer  bought  10  banvis  of  i>otatoes  containing 
2  bu.  3  }'k.  t  adi.  and  ivtail.-d  tli«-m  at  $.60  a  bi: 
How  much  diil  lie  receive  lor  them? 

4.  This  y.-ar  I  ITU!,  r-d  7  times  as  many  apples  as  pears 
from  my  garden,  and  I  gathered  40  bu.  1  pk.  of  ap- 
ples.   How  many  pears  did  I  gath 

6.  A  shoe  deaK-r  paid  *300  for  1  alf  boots,  at  $5 
a  pair.  How  many  cases,  of  12  pairs  rach.  did  IK 

'.'.   My  Lranl<-n  contains  ;)  A.,  and  my  door-yard  J$  A. 
My  garden  is  how  many  times  as  large  as  my  door- 
rd? 

7.  Ii%  I  of  apinr-apple  are  divided  among  5  childivn. 
what  part  of  a  pin.'-appl-  will  rat-h  child  h:r 

5.  A  woman  put  4  gal.  1  (\\.  1  pt.  of  catsup  into  pint 
and  quart  bottles,  using  2  times  as  many  of  the  1 

as  of  1 1  .    How  many  bottles  of  cacl , 

she  use  ? 

0.  A  dressmaker  used  11}  yd.  of  poplin,  in  makii. 
>kirt>  Q|  x'  \\alkinLr-dre8ses,  using  1.1   yd. 
1-nadth.     How  many  breadths  were  there  in 
.-kirt  l- 

JO.  A  farmer  finds  that,  if  he  divides  his  farm  equally 
among  his  6  children,  eaeh  of  them  will  hav 
acres  of  land.     What  is  the  size  of  his  farm  ? 

Multiplication  is  rqnMtcd  addition  of  the  same  part  or  num- 
ber, and  division  is  repeated  subtraction  of  the  same  part  or 
number.     Hence,  multiplication  is  the  reverse  of  division. 
11.  What  is  the  product  of  9  and  23  ?    Of  9  times  $2.30  ? 
;.'.  Tin*  multiplicand  is  '2  gal.  1  qt.,  and  the  multiplier  is  9. 

What  is  the  product  ? 

13.  Find  the  product  of  the  factors  6,  5,  and  8}. 
1$.  The  product  is  7f,  and  one  factor  is  5.     Find  the  other 
(factor 


CONVERSE    REDUCTIONS.  141 

15. .  The  product  of  three  factors  is  8|,  and  two  of  the  factors 
are  £  and  14.     What  is  the  other  factor  ? 

16.  The  product  is  6|,  and  the  multiplier  is  f .     What  is  the 
multiplicand  ? 

17.  The  multiplicand  is  2  bu.  1  pk.,  and  the  product  is  24  bu. 
3  pk.     What  is  the  multiplier  ? 

18.  The  divisor  is  6,  and  the  dividend  is  29.     What  is  the 
quotient  ? 

19.  The  dividend  is  29,  and  the  quotient  is  4f.     What  is  the 
divisor  ? 

SO.  The  divisor  is  6,  and  the  quotient  is  4£.     What  is  the 
dividend  ? 


SECTION    III. 


39.   Denominate  Tractions  to  Compound  Numbers. 

1.  A  MERCHANT  bought  two  pieces  of  linen,  paying  $J 
a  yard  for  one,  and  $T9C  a  yard  for  the  other.     How 
many  cents  a  yard  did  each  piece  cost  him  ? 

(See  Manual,  page  173.) 

2.  Reduce  •§  gal.  to  quarts  and  pints.     Methods,  pagciso. 
8.  What  compound  number  is  equal  to  3|  bu.  ? 

4.  How  many  inches  is  |  yd.  ?     Is  T^  yd.  ?     Are  j-  yd.  +  ^ 
yd.? 

5.  The  rows  of  vines  in  a  grapery  are  J  rd.  apart,  and 
the  vines  in  the  rows  are  }  rd.  apart.    What  is  the 
distance  in  feet  and  inches  between  the  rows  ? 

G.  What  is  the  distance  between  the  vines  ? 

7.  The  fence  which  incloses  my  orchard  is  -?-%  mi.  in 

length.     What   compound   number   expresses  the 

length  of  the  fence  ? 


142  CONVERSE    OPERATION     . 

tf.  II  «>w  many  square  feet  and  square  inches  are 

on  the  surface  of  a  mirror,  that  is  1 J  yd.  long  a: 

\<1.  wide? 
9.   H"W  many  cubic  feet  of  bricks  ar 

of  brick  wall,  if  ,1  «f  the  wall  is  mortar  ? 
70.  How  many  ounce  bullets  can  be  made  from 

of  lead  r 
77.  I  feed  my  cow  -f9  cwt  of  hay  daily.     H..W  many 

pounds  do  I  f« ••  >1  h«  r  ': 
/.'.  If  a  loenni'.tive  burns  ig  T.  of  coal  in  runn! 

mi.,  liow  many  pounds  does  it  burn  ? 
IS.  A  haker  used  $  bar.  of  flour  in  making  100  loaves 

of  bread.    How  many  pounds  of  flour  did  he  use  ? 
1<>  hours  of  work  a  day  an-  full  time,  how  much 

time  will  the  hands  work  daily,  in  a  fu-tnry  that  is 

running  on  5  tin. 

.' :.  When  the  time  of  sunrise  is  }  of  th<-  time  from  mid- 
night to  midday  or  noon,  at  what  hour  and  minute 

does  the  sun  rise  ? 

ioner  sold  T7,  of  a  gross  of  steel  pens.     II  -u 

many  dozen  pens  did  he  sell  r 
77.  A  mot!  !   ,85  of  a  roam  of  manilla 

supplying  her  customers  with  putt-  in.-.    llu\v  many 

quires  and  sheets  did  she  use  ? 

40i   Compound  Numbers  to  Denominate  Fractions* 

18.  The  value   of  the  old   New  England  shilling  was 
$.10  j.     What  fraction  of  a  dollar  was  it? 

/"'.  What  fraction  of  a  dollar  were  7  New  York  shillings, 
.-:• 

20.  One  day  a  hotel  cook  used  1  pt.  3  gi.  of  molass 
making  fruit -c;ike.     What  jiart  of  a  quart  did 
.      What  part  of  a  gallon? 


CONVERSE    REDUCTIONS.  143 

21.  1  pk.  5  qt.  of  beans  are  what  fraction  of  a  bushel  ? 

Aletliods,  page  ISO. 

22.  Express  4  bu.  3  qt.  1  pt.  by  a  mixed  number. 

23.  7£  in.  are  what  part  of  a  foot  ? 

24.  What  mixed  number  is  equal  to  72  rd.  4  yd.  1£  ft.  ? 

25.  2  sq.  ft.  72  sq.  in.  are  what  fraction  of  a  square  yard 

26.  What  fraction  of  an  acre  is  a  village  lot,  which  is  4 
rd.  front  and  9  rd.  deep  ? 

27.  If  4  shingles,  each  4  in.  wide,  are  laid  6  in.  to  the 
weather,  what  part  of  a  square  foot  do  they  cover  ? 

28.  A  block  of  marble  2  by  2|  by  1J  feet,  is  what  part 
of  a  cubic  yard  ? 

20.  60  Ib.  of  wheat  arc  a  bushel.    What  part  of  a  bushel 
are481b.? 

30.  How  much  must  I  pay  for  7  Ib.  10  oz.  of  butter,  at 
$.36  a  pound  ? 

31.  One  month  a  dairy-man  made  43  Ib.  12  oz.  of  cheese, 
from  the  milk  of  1  cow.    What  part  of  a  hundred- 
weight of  cheese  did  he  make  ? 

32.  If  school  is  in  session  5  days  of  the  week,  what  part 
of  the  school  week  has  passed,  at  noon,  Thursday  ? 

33.  In  45°  N.  latitude,  on  the  shortest  days  of  the  year, 
the  sun  is  above  the  horizon  8  h.  40  min.    What 
part  of  the  24  h.  is  day,  and  what  part  is  night  ? 

34.  One  season  Hudson  River  was  closed  by  ice  for  4  mo. 
12  da.    What  fraction  of  a  year  was  the  river  closed  ? 
What  part  of  a  year  was  it  open  ? 

35.  A  grocer  having  1  gro.  of  boxes  of  matches,  sold  6 
doz.  and  9  boxes  of  them.     What  part  of  the  whole 
gross  did  he  sell  ? 

86.  A  printer  used  13  quires  8  sheets  of  paper,  in  print- 
ing handbills.     What  part  of  a  ream  did  he  use  ? 


CHAPTER   YII. 
%f,.f&u*3fL*+3f^'  ^-^^^^^j^-^^sr 

|  HW***. 

PERCENTAGE. 


SECTION    I. 
41.  />///  v.  r/  •/•/".  r.v  .^.r#  ^v»r^  // 


THE  term  /Vr  On*  in  business  transactions  signifies  hun- 
dredths of  any  thing  or  number.  Thus,  1  JUT  rent  is  one  hun- 
dredth, or  1  of  every  hundred  ;  6  i»<  B  hundredths,  or 

6  of  every  hundred  ;  16f  per  cent  is  16|  hundredths,  < 

/.  How  many  hun.lredths  of  a  number  is  1  per  cent  of  it  ? 

I  I«>\v  many  liundrcdths  are  t   of  it  ? 

tl    r»|u-r(vnt?    7  per  cent?    8  per  cent?    10  per  cent? 
£.  Wliat  fr:u  tion  in  its  lowest  terms  expresses  15  \ 

15  hundredths  f 

5.  25  ])«  r  .nt  of  a  number  is  what  part  of  it  ?    50  per 
75  per  cent  ?    (See  Maniui,  pap?  ITU 

4,  6|  per  cent  of  a  numl>cr  is  what  part  of  it?     8J  p<  i 
i>  what  part  ?     12^  per  cent  is  what  part  ? 
What  part  of  a  number  is  10|  per  cent  of  it  ?    What  part 
is  66  \  per  cent  of 

6.  What  part  of  a  number  is  100  per  cent  of  it  ?    Is  1  1 
cent  of  it  ? 

7.  What  fraction  expresses  150  per  cent  of  a  number  :     11'^ 
per  cent  ?    140  per  cent  ?    112$  per  cent  .'    133J  per  . 

•s>.   N\  hat  part  of  a  number  is  4  per  cent  of  it  ?    Is  }  per  cent  ? 
|  per  cent  ?    -^  per  cent  ?    ^  per  cent  ?    ^  per  cent  ? 


GENERAL    CASES    OF    PERCENTAGE.      145 

9.  What  part  of  any  number  is  £  per  cent  of  it  ?    Is  £  per 

cent  ?    ^  per  cent  ?    |  per  cent  ?    f  per  cent  ? 
3frz/e?,  or  ftate  2>er  Cent,  is  the  number  which  expresses 
the  per  cent,  or  number  of  hundredths. 

The  term  Percentage  has  two  significations  : 
1st.  It  is  the  process  of  finding  any  per  cent  of  a  number ; 
2d.  It  is  the  name  of  the  result  of  the  computation. 
The  2?ase  is  the  number  on  which  the  percentage  is  com- 
puted. 

The  Amount  is  the  base  plus  the  percentage. 
The  ^Difference  is  the  base  minus  the  percentage. 
The  Commercial  Sign,  fa  signifies  per  cent. 
EXAMPLE.— 24$  of  50  cords  of  wood  is  .24,  or  -$&,  of  50 
cords,  or  12  cords.     In  this  example,  24$  is  the  rate;  50  cords, 
the  base;  12  cords,  the  percentage;  62  cords  (=  50  +  12),  the 
amount,  and  38  cords  (=  50  —  12),  the  difference. 

Per  cent  may  be  applied  to  any  number,  great  or  small,  con- 
crete or  abstract.     Thus, 

40    per  cent  of  1  bushel  =  .40  bu.  =  -^  bu.  =  £  bu. ; 
88        "        "    27  miles  =  .88    =  -flfr  =  ff  of  27  mi. ; 
14£      "        "     395  days  =  .14£  =  &  of  395  da. ; 
7        "        "    $85.42     =  .07    =  T^  of  $85.42 ; 
65        "        «  =  .65    =     fa  =  H  of  93*- 


SECTION     II, 
THE   FIYE    GEJV&'Rd.L    CASES    OF 


42.   Base  and  Rate  given,  to  find  Percentage. 

1.  How  much  is  6$  of  $100  ? 

2.  A  man  bought  a  horse  for  $125,  and  paid  20$  of  it 
down.    How  much  money  did  he  pay  down  ? 

8.  A  farmer  raised  500  bu.  of  corn,  and  sold  25%  of  it. 
How  many  bushels  did  he  sell  ?    Methods,  page  iso. 
12 


M';  PERCENT  \ 


-}.  \ty%  of  an  army  of  90,000  men  \\viv  killed  and 
wounded  in  an  engagement  How  many  weiv  killed 
and  wounded  ? 

I  rom  a  yard  containing  150  cattle,  66|<£  were  sold 
he  first  market  day.     How  many  were  sold  '-. 

fruit  grower  sent  75  baskets  of  peaches  to  ni; 
but  In  fore  they  were  sold,  8#  of  them  were  sj. 
How  many  baskets  did  he  lose  ? 
much  ia 


7.  -V   of  HOrd.  of  WOOd? 

8.  8#  of  250  yd.  of  sheetings? 

9.  3£  of  50  thousand  shingles? 


10.  12J*  of  $75  ? 

11.  80£  of  190  mi.  ? 
IS.  554  of  230  bu,  ? 


43.   Base  and  Percentage  given,  to  find  Rate. 

13.  A  sewing-machine  winch  cost  $100,  was  sold  fur 
$80.    What  %  of  the  cost  did  it  sell  f 

14.  A  sheep  grower  having  450  sheep,  sold  150  of  tlu-m. 
What  %  of  his  flock  did  he  sell  ?    Method*,  page  iso. 

'.  A   boy  having   15   apples,  ;_ 

What  %  of  his  apples  did  he  give  away? 

1>>.  A  man  having  $50,  paid  out  $10  of  it  for  provi 
What  ^  of  his  money  did  nd  ? 

17.  A  landlord  rents  a  honse  worth  $1,250,  for  £ 
\var.     What  ^  on  its  value  does  the  house  rent 

18.  A  farmer  pays  $3  per  acre,  for  the  use  of  land  vulu« -d 
at  $50  per  acre.    What  ^  on  the  valui.-  of  the  land, 
does  he  pay  for  the  use  of  it  ? 

10.  V/ha:      of  oOO  bu.  an-  50  bu.  ? 

X.W.   What  ',  of  7.")  melons  an-  l."i  intU.ns  .' 

SI.  $119  are  what  %  of  $340  ? 

SS.  1  bu.  3  pk.  are  what  %  of  6  bu.  1  pk.  ? 

S3.  f  of  an  hour  niv  what  ^  of  f  of  an  hour  ? 


GENERAL    CASES    OF    PERCENTAGE.      147 
44.    Rato  and  Percentage  given,  to  find  Ease. 

24.  From  a  certain  regiment,  100  men  are  detailed  on 
picket  duty,  and  the  number  detailed  is  12£  %  of 
the  whole  number  who  are  fit  for  duty.    How  many 
men  of  that  regiment  are  fit  for  duty  ? 

2-j.  A  gentleman  sold  his  house  and  lot  for  25%  above 
cost,  and  made  $500.  How  much  did  the  property 

COSt  ?      Methods,  page  180. 

26.  From  1  day's  sales  a  merchant  received  $133,  which 
was  1%  of  his  weekly  sales.    How  much  were  his 
receipts  for  the  week  ? 

27.  A  farmer  carried  to  mill  10  bushels  of  wheat,  which 
was  \%  of  his  whole  crop.     How  many  bushels  did 
he  raise  ? 

25.  This  year  a  hop  grower  sold  his  hops  at  24  cents  a 
pound,  which  was  80$  of  the  price  he  received  last 
year.    At  what  price  did  he  sell  his  crop  last  year  ? 

29.  A  certain  school  closed  its  winter  term  with  115 
pupils,  which  was  92$  of  the  number  with  which 
the  term  commenced.  With  how  many  pupils  did 
it  commence  ? 

SO.  $600  arc  6$  of  what  sum  of  money  ? 

31.  800  is  10$  of  what  number  ? 

82.  1,500  is  33£  of  what  number  ? 


45     Base  and  Rate   given,  to  find  either  Amount  or 
Difference. 

33.  If  maple  wood  is  worth  20$  more  than  oak,  and 
oak  sells  at  $7.50  per  cord,  how  much  is  a  cord  of 

maple  WOrth  ?      Methods,  page  ISO. 

34.  A  gentleman  having  $600,  paid  20$  of  it  for  a  gold 
watch.     How  much  had  he  remaining  ? 


148  I'KKr  KNTAGE. 


.    ^••ntl'-man   liavinir   x;;,o   dcjio-iK'.l    in   a   bank, 
chtrkrd  out  33  *#  of  it     How  much  r>  in 
deposit  ? 

36.  A  merchant  bought  Memmac  prints  at  20  cents  a 
yard,  but  the  next  y  as  obliged  to  pay 

more  for  the  same  class  of  goods.    How  much  did 
he  pay  per  yard  ? 

87.  A  merchant  started  in  bu.-'. 

$2,400,  and  added  to  it  33J#  in  two  years.    A\ 
was  his  capital  at  the  <  \  pirat  ion  of  the  second  y 

38.  The  base  is  35,  and  the  rate  is  25£.   What  is  the  amount  \ 
What  is  the  difference  ? 

i-l  the  amount,  and  also  the  diffcrcnc  ie  base 

is  |  and  the  rate  is  8J£ 

46.   Amount  or  Difference)  and  Rate  given,  to  find  Base. 

40.  A  speculator  bought  cheese  at  two  factories,  buying 
9,000  Ib.  at  one,  which  was  50$  more  than  he  bought 
at  UK  oth,-r.     How  much  did  he  buy  at  the  second 

factory  ?      Method.,  page  18O. 

41.  A  man  on  a  journey  travel  <>f  tlu    wlml- 

'  by  stage,  and  the  remainder,  which  was  140 
mile*,  by  railroad.    How  many  miles  did  h 

.;  ..  A  widow  expended  25j£  of  her  income  for  hi  r 
port,  and  saved  $60  a  month.     What  wa.s  lu-r  in- 
come? 

43.  A  physician's  practice  is  worth  :><>;  m.>r 

than  it  was  last,  and  this  year  it  is  worth  $2 
How  much  was  his  practice  worth  last  year  ? 

44'  87  cows  are  116£  of  how  many  cows  I 

45.  1  Ib.  11  oz.  are  112#  of  what  number? 

46.  $44  are  22^  of  how  many  dollars  T 

47.  57  ft.  are  95<  of  how  many  feet  ? 


APPLICATIONS    OF    GENERAL    CASES.     149 

SECTION    III. 

SPECIAL   APPLICATIONS    Of1  THE  FIYE 
GEJYEKAZ,    CASES. 

47.   Insurance* 

Insurance  is  a  security  against  loss  or  damage  within  a 
given  time,  guarantied  to  one  party  by  another,  for  a  specified 
consideration. 

7  '(dualion  is  the  sum  for  which  property,  life,  or  health  is 
insured. 

Premium  is  the  sum  paid  for  the  insurance. 

The  Policy  is  the  contract  between  the  insurer  and  the 
insured. 

In  computations  in  insurance,  valuation  is  the  base,  premium 
is  the  percentage,  and  rate  %  is  the  rate. 

1.  At  \%  premium,  how  much  must  be  paid  for  an 
insurance  of  $600  on  a  quantity  of  grain  ? 

2.  A  gentleman  effected  an  insurance  of  $1,500  on  his 
house,  at  2%  premium.    How  much  did  he  pay  for 
his  policy  ? 

3.  A  cabinet  maker  paid  k%  for  an  insurance  of  $3,000 
on  his  stock  and  shop.     How  much  did  the  insur- 
ance cost  him  ? 

4.  What  must  be  paid  for  an  insurance  of  $5,000  on  a 
stock  of  goods,  at  \\%  ? 

5.  A  produce  dealer  paid  $25  for  an  insurance  of 
$5,000,  on  a  cargo  of  produce.     What  %  premium 
did  he  pay  ? 

6.  A  hardware  merchant  paid  an  insurance  agent  $50 
premium,  for  a  policy  of  $2,500,  on  a  stock  of  stoves. 
What  %  did  he  pay? 

7.  What  %  premium  does  that  man  pay,  who  pays  $9 
for  a  policy  of  $1,200,  on  his  house  and  furniture  ? 


150  i'i:i:»  i:  XT  AGE. 

8.  If  a  lawyer  pays  $15  for  an  insurance  on  his  clothing 
and  library,  at  f  $,  what  amount  does  he  get  insu 

9.  A  fanner  paid  an  agent  $8  for  insuring  his  barn 
and  its  contents,  at  \%.    What  amount  did  he  get 
insured  ? 

48.    Commission. 

hajiffcitf.  CbmmtutOM  .)/'/•<•//,/,//.  /  ;/,  -A//%  or  ^Bro- 
ker is  a  person  who,  by  .  buys  and  sells  goods,  or 

transacts  other  financial  business  for  another. 

/  is  the  person  or  party  for  whom  an  agent 
transacts  business. 


is  the  sum  paid  an  agent  or  commission  -mer- 
chant tor  transacting  business, 

hi  (Deputations  in  commission,  the  sum  expended  »•: 
lected  by  the  agent,  for  tlic  principal,  is  the  base;  commission 
is  tin-  percentage  ;  rate  £  is  the  rate;  and  the  sum  on  which 
commission  is  computed,  plus  the  commission,  is  the  amount 

10.  A  person  collects  accounts  amounting  to  $50< 

ives  10$  on  the  money  collected  for  his  sen 
How  much  does  he  receive  ? 

i  air-  in  in  New  York  buys  goods  to  the  amount 
of  $3,000,  and  receives  5$  commission.  Huw  much 
does  he  r 

12.  A  planter  sends  40,000  Ib.  of  cotton  to  his  corres- 
pondent in  New  York,  who  sells  it  at  15  cents  a 
pound,  and  retains  8}£  commission.    How  much 

I  tlu-  plunUT  : 

13.  A  collector's  fees  are  \%  on  all  sums  paid  to  him 
within  30  days  after  receiving  his  warrun:. 

on  all  amounts  collected  th<: 
his  town  are  $15,000,   $5,000  of  which 
within   the   30  days,   and   the  balance   there;: 
What  ai\-  his  ices  for  collecting? 


APPLICATIONS    OF    GENERAL    CASES.     151 

14.  A  druggist  sent  his  broker  $630  with  which  to  buy 
goods,  after  deducting  his  commission  of  5$.  How 
much  did  the  broker  expend  for  goods  ? 

1-1.  A  manufacturer  sends  to  a  wool  broker  $2,600  with 
which  to  purchase  wool,  allowing  him  2%  brokerage 
on  the  money  paid  out.  How  much  money  will  the 
broker  expend  for  wool  ? 

1G.  A  book  buyer  in  New  York  receives  $800  to  expend 
for  books  for  a  library,  after  deducting  his  commis- 
sion of  12|^.  How  much  will  he  expend  ? 

17.  A  brewer  allows  4$  for  buying  hops,  and  sends  his 
broker  $5,200.    How  many  pounds  of  hops,  at  25 
cents  a  pound,  will  he  receive  ? 

18.  A  collector  received  $40  for  collecting  bills,  at  5% 
commission.    How  much  money  did  he  collect  ? 

10.  A  horse  dealer  received  $15  for  selling  a  horse,  which 
was  10$  of  his  value.  For  how  much  was  he  sold  ? 

49.   Profit  and  Loss. 

'Profit t  in  business,  is  the  sum  above  cost  for  which  goods 
are  sold. 

Ztoss  is  the  sum  below  cost  for  which  goods  are  sold. 

In  computations  in  profit  and  loss,  the  cost  is  the  base  ;  the 
profit  or  loss  is  the  percentage  ;  the  rate  %  is  the  rate,  and  the 
selling  price  is  the  amount  or  difference. 

20.  Last  year  a  farmer  had  450  sheep,  and  his  flock  has 
increased  30%  in  the  year.     How  many  more  sheep 
has  he  than  lie  had  last  year  ? 

21.  A  hen  hatched  a  brood  of  15  chickens,  but  lost  40$ 
of  them.     How  many  chickens  did  she  lose  ? 

22.  A  grocer  sold  white-fish  that  cost  $16  a  barrel,  at 
50$  profit.    How  much  did  he  gain  on  a  pound  ? 


1  .'•'.'  PERCENTAGE. 

.'•''.  The  bread  made  from  a  barrel  of  flour  weighs  40$ 
more  than  the  flour.  How  many  pounds  more  does 
it  weigh  ? 

24.  A  man  sold  a  city  lot  which  cost  him  $160,  at  an 
advance  of  212^$.  How  much  did  IK-  pi: 

. '.  A.  card  of  green  beech  wood  weighs  6,000  Ib.,  and  it 
loses  27$  of  its  weight  in  seasoning.  How  much 
liirhh-r  is  a  cord  of  dry  beech  than  a  cord  of  green  ? 

26.  A  merchant  sold  broadcloth  that  cost  him  $5}  a 
yard,  at  a  loss  of  33J$.  How  much  did  he  lose  on 
a  yard  ? 

\  i-iiys  sugar  at  $.10  a  pound,  and  sells  it  at 

a  profit  of  30$.    For  how  much  does  he  sell  it  ? 

28.  I  bought  6  cords  of  wood  for  $10.    At  what 
per  cord  must  I  sell  it,  to  make  20#  ? 

29.  A  grocer  sold  t  a  that  cost  him  $.78  a  poun> 
loss  of  15%.    What  did  he  get  a  pound  for  it  ? 

.    \  -]n  c  ulator  bought  butter  at  $.35  a  pound,  but  was 

obliged  to  sell  it  at  a  loss  of  12J$.    For  how  much 

did  he  sell  it? 
81.  A  gentleman  bought  a  house  and  lot  for  $1,600,  paid 

10$  for  repairs  and  painting,  and  sold  it  for  15# 

profit    How  much  did  he  get  for  it  ? 
..   A  manufacturer  finds  that  it  costs  him  $1.20  a  yard 

to  manufacture  his  cloth,  and  he  wishes  to  sell  it  at 

a  profit  of  25$.    How  much  will  he  make  a  yard, 

and  how  much  a  yard  will  he  sell  it  for  ? 
S3.  A  gentleman  sold  a  horse  and  harness  for  $180, 

which  was  10^  less  than  cost.     How  much  did  they 

cost  him  ? 
84.  A  manufacturer  sold  damaged  cloth  at  cost,  or  $1.50 

a  yard,  which  was  33]$  below  the  marked  price. 

What  was  the  marked  price  ? 


APPLICATIONS  OF    GENERAL    CASES.     153 

So.  A  silversmith  sold  tea-spoons  at  $1.65  each,  and 
made  25^.     How  much  did  they  cost  him  ? 

36.  A  jeweler  sold  a  watch  for  $69,  which  was  15$  ad- 
vance on  the  cost.     How  much  was  the  cost  ? 

37.  A  grocer  bought  sugar  at  $.08  a  pound,  and  sold  it 
at  $.10.    What  %  did  he  make  ? 

38.  A  book-seller  sold  a  book  for  $1.00,  that  cost  him 
$.75.    How  much  %  did  he  make  ? 

39.  A  carman  sold  a  truck  for  $87A,  which  cost  him 
$100.    At  what  %  less  than  cost  did  he  sell  it  ? 

40.  A  flour  dealer  bought  flour  for  $6  a  barrel,  and  sold 
it  for  $7.    What  %  did  he  make  ? 

41.  What  %  does  a  grocer  make,  by  selling  eggs  at  \  of 
their  cost  ? 

Jt2.  If  kerosene  is  bought  at  f  of  the  market  price,  and 
sold  at  10%  below  the  market  price,  what  %  is  lost  ? 


50.   Stocks. 

A  Corporation  is  a  company  established  by  law,  having 
power  to  transact  business  as  an  individual. 

Stock  is  the  property  invested  in  the  business  of  a  corpora- 
tion. 

A  Share  is  one  of  the  equal  parts  into  which  the  stock  of  a 
corporation  is  divided.  It  is  usually  $100. 

The  'Par  Value  of  stock  is  the  sum  stated  in  the  certifi- 
cate ;  and 

The  Market  Value  is  the  sum  for  which  it  will  sell. 

Stock  is  jit  jPar  when  the  market  value  is  the  par  value, 
or  100#. 

Stock  is  Above  3?ar  when  the  market  value  is  above  the 
par  value,  or  more  than  100$  ;  and 

Stock  is  Selow  *Par  when  the  market  value  is  below  the 
par  value,  or  less  than  100$. 


154  PERCENTAGE. 


is  the  excess  over  100^  in  the  value  of  stock 
that  is  above  par;  . 

Discount  is  the  deficiency  under  100#  in  the  value  of 
stock  that  is  below  par. 

A  .N'A"-X-  ///••'/•-  /•  ot  Stock  ./-,'>'<•  r  is  a  person  who  deals 
in  stocks. 

-//'•  is  the  commission  paid  to  stock  brokers  for 
luiying  and  selling  stocks  for  ot 

In  rnmput:itions  in  stocks,  the  par  value   U  the  La 
premium  or  the  discount  is  the  percentage,  the  rate  $  \<  the 
rate,  and  the  market  value  is  the  amount  or  differ 

43.  A  stock  jobber  bought  $3,000  w.  I  J.  R.  stock, 
and  sold  it  at  a  loss  of  10<£.     How  much  did  he  lose  ? 

44.  For  how  much  did  he  sell  it  ? 

silver  is  at  a  premium  of  15&  how  much  currency 
will  a  man  have  to  pay  for  $50  in  silv 

46.  A  broker  j»aid  $2,900  in  bills  for  gold,  when  gold  wa.s 
at  a  premium  of  45$.     How  much  gold  did  he  buy  ? 

47.  He  sold  his  gold  at  a  premium  of  5(#.    How  much 
did  he  make  in  the  tu..  transactions? 

.   \VlKitistheiiKirketvalucofashareofmining8tock, 

that  sells  at  32  j£  below  par? 
40.  A  brok  ved  $1,750  for  15  shares  of  insurance 

stock.     What  was  the  market  value  of  a  sh;; 
50.  A  man  paid  $262.1  for  stock  in  a  toll-bridge,  at  12  # 

discount    How  many  shares  did  he  buy? 

51.   Taxes. 

7'ff.rcs  arc  sums  of  money  assessed  upon  persons  and  prop- 
erty, to  meet  public  expenses, 

Property  is  of  two  kinds:  '/'•  -/  /;VA//V.  or  houses  and 
Ian.  Is  ;  and 

fersonal  ^Property,  or  movable  property. 


INTEREST.  155 

In  computations  in  taxes,  the  valuation  of  property  is  the 
base  ;  the  rate  %  is  the  rate  ;  and  the  tax  is  the  percentage. 

51.  A  tax  of  $250  was  levied  on  a  village,  in  which  the 
real  estate  was  assessed  at  $19,000,  and  the  personal 
property  at  $6,000.     What  was  the  rate  %  of  tax  ? 

52.  The  taxable  property  in  a  certain  school  district  is 
valued  «t  $20,000,  and  a  tax  of  $50  is  voted  to  repair 
the  school-house.    What  is  the  rate  %  of  the  tax  ? 

53.  A's  property  is  assessed  at  $2,500.    How  much  is 
his  tax  ? 

54.  B  is  assessed  for  $3,000.     How  much  is  his  tax  ? 

55.  C  is  assessed  for  84,500.     What  is  his  tax  ? 

56.  How  much  is  D's  tax,  his  property  being  assessed  at 
$1,500  ? 

57.  E  is  assessed  for  $8,500.    How  much  must  he  pay  ? 

58.  A  machine  costing  $150,  is  put  into  a  planing-mill 
owned  by  8  men,  whose  shares  of  the  capital  arc, 
respectively,  $600,  8400,  $1,200,  $500,  $1,500,  $800, 
$300,  and  82,200.     How  much  of  the  cost  of  the 
machine  must  each  partner  pay  ? 


SECTION    IV. 


Interest  is  the  sum  paid  for  the  use  of  money. 

^Principal  is  the  sum  for  the  use  of  which  interest  is  paid. 

Amount  is  the  sum  of  principal  and  interest. 

(Rate  per  Cent  per  Annum  is  the  interest  on  $1  for  1 
year. 

In  computations  in  interest,  principal  is  the  base  ;  the  prod- 
uct of  rate  %  per  annum  and  time  expressed  in  years,  is  the 
rate  ;  and  interest  is  the  percentage.  Interest  is  the  product 
of  the  three  factors,  principal,  rate,  and  time. 


PERc  i:\TAGE. 

52.   Interest  for  Tears,  or  Months,  or  Days. 

/.  What  is  tli..-  int.-r.-st  of  $75  for  2  years,  at  - 

.'.  What  is  ilit-  interest  of  $500  for  3  years,  at  7#? 

3.  A  gentleman  has  a  mortgage  for  $1,000,  diu-  in  4 
years,  at  1%.    How  much  interest  will  he  receive  ? 

4-  A  man  purchased  a  city  house  and  lot  for  $4,500, 
paying  $1,500  in  cash,  and  giving  a  mortgag< 
tin-  balance  due  in  5  years,  at  8$,  interest  payable 
annually.    How  much  interest  did  he  pay  yearly? 

5.  How  much  money,  principal  and  interest,  did  lie 
pay  for  the  property  ? 

6.  What  part  of  a  year  is  1  month?    Arc  2  months!    6 
months  ?    8  months  ? 

7.  9  months  are  what  part  of  a  year  ?    4  months  ?    7  months  ? 

8.  The  interest  of  any  sum  of  money  for  10  months  will  l>o 
what  part  of  the  interest  of  the  same  sum  for  1  year? 

0.  The  interest  for  5  months  will  be  what  part  of  1  year's 

interest? 

/".  What  is  the  interest  of  $450  for  4  months,  at  G 
11.  At  7   .  what  is  the  interest  of  $50  for  3  months  ? 
/.'.   What  part  of  the  principal  will  cijnal  the  in 
for  9  months,  at  6 

13.  How  much  intn,  st  must  be  paid  for  the  use  of  $120 
for  10  months,  at 

14.  What  part  of  a  month,  or  30  days,  is  1  day  ?    Are  8  days  ? 
8  days?     10  days?    20  days? 

15.  14  days  are  what  part  of  a  month  ?    15  days  ?    24  days  ? 

16.  The  interest  of  any  sum  of  money  for  25  days  will  be  what 
part  of  the  interest  of  the  same  sum  for  1  month  ? 

/:.   What  part  of  the  intenst  f.-r  1  month  is  the  interest  for 

18  days  ?     Is  the  interest  for  12  days  ?    For  28  days  ? 
7,v.  What   is  the  interest  on  a  note  for  $75,  due  in  15 
days,  at  • 


APPLICATIONS    OF    GENERAL    CASES.      157 

19.  I  borrowed  6150  for  3  weeks,  at  10^.    How  much 
interest  did  I  pay  ? 

20.  At  24^b  per  annum,  what  is  the  rate  %  per  month  ? 
Per  day  ? 

21.  A  broker  loaned  $750  for  18  days,  at  2$  per  month. 
How  much  interest  did  he  receive  ? 

53.   Interest  for  any  Given  Time. 

22.  What  part  of  a  year  are  7  mo.  15  da.  ?    4  mo.  24  da.  ? 

23.  The  interest  of  any  sum  of  money  for  6  mo.  18  da.  will  be 
what  part  of  the  interest  of  the  same  sum  for  1  year  ? 

2J^  How  much  interest  has  accrued  on  an  account  of 
$45,  which  lias  been  due  2  yr.  G  mo.,  at  §%  ? 

2.j.  At  7$,  how  much  must  I  pay  for  the  use  of  $150 
for  1  yr.  4  mo.  ? 

J'>.  What  is  the  interest  of  $750  for  3  mo.  G  da.,  at  6$? 

27.  A  mechanic  while  building  a  house,  borrowed  $380 
for  7  mo.  15  da.,  at  8$.    How  much  interest  did  he 
pay? 

28.  How  much  will  $30  gain  in  2  yr.  2  mo.  20  da.,  at 
6$  ?    To  how  much  will  it  amount  ? 

29.  At  \%  a  month,  how  much  will  a  banker  receive 
for  the  use  of  $100,  for  2  yr.  5  mo.  10  da.  ? 

80.  Find  the  interest  of  $150  for  1  yr.  6  mo.  12  da.,  at 


31.  How  much  interest  has  accrued  on  a  mortgage  for 
$300,  which  has  been  running  4  yr.  4  mo.  15  da.,  at 
7#? 

32.  A  man  paid  6^  interest  on  a  note  for  $450,  which 
had  been  due  2  yr.  10  da.    How  much  interest  did 
he  pay  ? 


158  i- 1:  it  0  i:  .>  T  A 

54.   Converse  Operations  in  Interest* 

will  $50  gain  $15  int.  :  mo.? 

34.  At  what  per  cent  will  $30  gain  $4/.)o  interest  in  1  yr 

9  mo.  ?      (See  Manual,  page  178.) 

55,  If  1  pay  *:.  1   i  T  the  use  of  $200  for  :J  yr.  -1  mo.  15 
da.,  wh..  :it  do  I  pay? 

\t  what  \  will  $50  amount  to  $G0.50  in  3  years? 

the  amount  of  $250  for  4  years  is  $310,  what  is 
the  rate  of  interest  ? 

I  loan  $500,  and  at  the  end  of  2  yr.  C  mo.  receive 
$587.50,  what  rate  of  interest  d«  •  I 

i  ho  interest  on  $25  for  20  years  is  $25,  what 
rate#? 
40.  At  what  per  cent  will  $73  gain  $75  interest  in  1 

.:   what  per  cent  will  any  given  principal  donhle 
itself  in  10  years  ?    In  12}  years  ? 
At  Gf/,  what  principal  will  gain  $24  in  8  years  ? 
What  principal  will  <;ain  $28  in  8  years,  at  7#? 
; ;.  What  sum  will  earn  $35  interest  in  4  years,  at 
;   .  At  1J$  a  month,  what  principal  will  gain  $300  in- 
n-rest in  5  yr.  G  mo.  20  da.  ? 

.   .  What  principal  will  amount  to  $171  in  2  yr.,  at7#? 
.;;.  What  sum  of  money  put  at  inter  -HI  at  \\  foe 
6  mo.,  will  amount  to  $52  ? 

48.  At  5£,  what  principal  will  amount  to  $480  in  4 

49.  The  time  is   ID  yr.  8  mo.,  the  rate  is  6$,  and  the 
amount  is  $82.     What  is  the  principal? 

50.  In  what  time  will  $90  gain  $10.80,  at  6#? 

51.  In  what  time  will  $125  gain  $25,  at  I 

.    Kor  how  long  a  time  must  $75  be  at  inu  : 
to  gain  $16  ? 


DISCOUNT.  159 

53.  In  what  time  will  any  sum  of  money  double  itself, 
at  5$  ?  At  6$  ?  At  *t%  ?  At  8%,  ?  At  10$  ? 

&£.  For  how  long  a  time  must  $250  be  at  interest,  at 
G£,  to  amount  to  $300  ? 

JJ.  In  what  time  will  $64,  at  7#,  amount  to  $76.20  ? 


SECTION  V. 

DISCO  UJYT. 
55.   Commercial  Discount 7  or  Per  Cent  Off. 

The  Face  of  an  obligation  is  the  sum  to  be  paid  when  the 
obligation  is  due. 

Commercial  %)iscotent,  or  (Per  Cent  Ojf,  is  a  deduc- 
tion from  the  face  of  the  obligation,  of  some  $  agreed  upon, 
without  regard  to  time. 

In  computations  in  commercial  discount,  invoice  price,  or 
the  face  of  the  obligation,  is  the  base  ;  rate  %  off  is  the  rate  ; 
and  the  commercial  discount  is  the  percentage. 

1.  I  bought  articles  that  I  retailed  at  $1.00,  at  \  off 
What  %  did  I  make  ? 

2.  A  book-seller  buys  books  that  retail  at  $.80,  at  j  off. 
What  %  does  he  make  ? 

3.  A  merchant  bought  linen  which  retailed  at  $.50  a 
yard,  at  50$  off.    What  %  did  he  make,  by  selling 
it  at  the  regular  price  ? 

4.  The  proprietor  of  a  variety  store  buys  toys  that  re- 
tail at  $.12,  at  J  off.    What  %  does  he  make  ? 

~>.  A  stationer  buys  ink  that  retails  at  $.10  a  bottle,  at 

20$  off.     What  %  does  he  make  ? 
G.  A  merchant  bought  $4,000  worth  of  goods,  on  a 

credit  of  6  months,  but  got  a  discount  of  5$  off  for 
h.     What  was  the  cash  cost  of  his  goods  ? 


160  PEK<  i:  N  T  \ 

f  goods  are  sold  at  1UO£  less  than  cost,  how  much 
do  they  bring  ? 

8.  If  slates  are  sold  at  wholesale,  at  40#  off  from  retail 
or  list  prices,  and  a  further  discount  of  5#  off  is 
made  for  cash,  what  is  the  total  %  off  from 
vs,  for  cash  ? 

.  to  buy  goods  at  30£  off  and  5% 
off  for  cash,  or  to  buy  at  5£  off  and  30^  off  for  cash  ? 

56.   True  Discount. 

Discount  is  a  sura  deducted  for  the  payment,  before  it 
becomes  due,  of  a  note  or  otli  •  drawing  interest 

present  )*'<>/•///.  <>r  7'/-»<°ccds,  is  the  face  of  an  obliga- 
tion less  the  discount. 

In  computations  in  a  discount,  present  worth  or  proceeds  is 
the  base  ;  the  product  of  the  rate  per  cent  per  annum  and  the 
\pressed  in  years,  is  the  rate  ;  the  face  of  the  obligation 
is  the  amount ;  and  the  discount  is  the  percentage. 

10.  How  much  must  be  discounted  for  the  present  pay- 
ment of  a  note  for  $84,  il;  are,  money  being 
worth  6 

/  /.  I  bought  a  note  for  $207,  due  in  G  months,  at  1% 
discount  How  much  did  I  pay  for  it  ? 

/.'.  A  man  sold  property  for  *!.»>•..»:>.  taking  notes  cltir  in 
3  months,  and  tlu-n  sold  the  notes  at  10$  discount 
for  cash.  How  much  discount  did  he  give  ?  How 
much  cash  did  ho  roe 

13.  A  broker  bought  a  note  for  $412,  due  in  2  months, 
at  a  discount  of  \\%  a  month.     How  much  did  he 
pay  for  it  ? 

14.  I  owe  $530,  due  in  4  mo.  15  da.,  and  I  find  ] 

hn y  the  debt  at  1G^  discount  for  cash.    How  much 
cash  will  pay  the  debt? 


REVIEW     PROBLEMS.  161 

SECTION    VI. 


1.  Only  J  of  a  certain  regiment  are  fit  for  duty.    What 

%  are  on  the  sick  list  ? 
,'.  A  teacher,  whose  salary  is  $800  a  year,  expends  $700 

in  support  of  his  family.    What  %  of  his  salary  docs 

he  save  ? 

3.  A  father  gave  to  each  of  2  sons  25$  of  a  farm  con- 
taining 500  acres.     How  much  land  was  given  away, 
and  how  much  had  he  remaining? 

4.  A  farmer  bought  a  cow  for  $GO,  and  sold  her  so  as  to 
gain  20$.     How  much  did  he  gain  ? 

5.  The  interest  received  on  $1,000  for  10  years  was  T75 
of  the  principal.    What  was  the  rate  %  of  interest 
received  ? 

G.  Two  regiments  went  into  battle  with  800  men  each. 
After  the  battle,  one  mustered  G25  men,  which  was 
25$  more  than  the  other  mustered.  How  many  men 
did  the  second  regiment  muster  ? 

7.  A  produce  dealer  sends  to  his  factor  in  Boston 
25,000  Ib.  of  butter,  which  he  sells  at  $.20  a  pound, 
and  charges  7$  commission  and  guaranty.     How 
much  does  the  dealer  receive  for  his  butter? 

8.  A  grape-grower  refused  $.15  a  pound  for  his  grapes, 
but  afterward  sold  them  at  1G*$  less.    How  much 
did  he  get  a  pound  for  them  ? 

0.  A  book-seller  sold  goods  to  the  amount  of  8900  in 
one  month,  at  an  average  profit  of  25$.  What  was 
the  cost  of  his  goods  ? 

10.  At  what  $  will  $75  amount  to  $87  in  4  years  ? 

13 


162  PERCENTAGE. 

11.  \  steam-boat  is  owned  by  5  men,  A  owni: 

shares,  B  100  shares,  C  150  shores,  D  200  shares, 

1  £  275  shares.    An  assessment  of  $4,000  is  made 

for  repairs.    How  much  must  each  stockholder  pay  ? 

2  '.  What  principal  will  gain  $76  in  6  yr.  4  mo.,  a 

13.  If  I  receive  $2,736  for  24  shares  of  bank  li 
is  the  value  of  1  share  ? 

\  t  8^,  in  how  long  a  time  will  the  interest  on  $30 
amount  to  $12  ? 

r,  in  how  long  a  time  will  *i 
$14'.'. 

16.  A  grocer  buys  molasses,  which  retails  at  $.80  a  gal- 
lon, for  20^  off.    What  %  does  he  mak 

17.  14  f  per  cent  is  what  fraction  of  a  number  ? 

18.  A  policy  of  $150,000  was  obtained  on  a  Teasel  and 
cargo,  for  the  voyage,  at  g£.    IIow  much  was  paid 
for  the  insurance  ? 

19.  A  country  merchant  has  |  of  his  capital  invested  in 
dry  goods,  730  of  it  in  groceries,  £  in  hardware,  and 
the  balance  in  crockery.     What  %  of  his  capital  is 
invested  in  each  of  these  classes  of  goo< 

SO.  In  the  year  1863,  a  merchant  sold  cotton  goods  at 
33 \%  above  cost,  and  received  $.36  a  yard  for  them. 
How  much  did  they  cost  him  JKT  yard  ? 

21.  If  I  burn  4  T.  of  coal  during  the  summer  months, 
and  what  I  burn  in  the  summer  is  75£  of  as  much 
as  I  burn  in  the  winter,  how  much  coal  do  I  burn 
in  a  year  ? 

28.  A  fruit  dealer  sold  10  baskets  of  peaches,  that  cost 
$1.25  per  basket,  at  12J£  below  cost  How  much 
did  he  lose  on  them  ? 


REVIEW    PROBLEMS.  163 

23.  A  merchant  bought  cassimerc,  at  auction,  at  28;}$ 
below  the  manufacturer's  price,  paying  $1.25  a  yard 
for  it.    He  retailed  it  at  32$  above  manufacturer's 
price.    What  was  his  retail  price  ? 

24.  A  stationer  sold  paper  that  cost  him  $.75  a  ream,  for 
$1.50.    What  %  profit  did  he  make  ? 

25.  A  boy  bought  apples  at  the  rate  of  3  for  5  cents,  and 
sold  them  at  the  rate  of  2  for  3  cents.    What  %  did 
he  make  ? 

26.  A  dairy-man  contracted  his  cheese  at  $.15  a  pound, 
but  at  the  time  of  delivery  this  price  was  25$  below 
the  market  price.    What  was  the  market  price  ? 

27.  An  importer  in  Philadelphia,  who  pays  16-$  for 
buying  and  insurance,  remits  to  his  agent  in  London 
$5,684.    How  many  dollars'  worth  of  goods  ought 
he  to  receive  ? 

28.  If  gold  is  at  a  premium  of  174&  how  much  cur- 
rency will  a  man  receive  for  $80  in  gold  ? 

29.  How  much  are  5  shares  of  bank-stock  worth,  at 
18 \i  advance? 

30.  A  Louisiana  planter  paid  a  New  Orleans  merchant 
an  account  of  $450,  which  had  been  due  3  yr.  7  mo. 
C  da.   What  was  the  interest  on  the  account,  at  5$  ? 

31.  If  I  receive  $63  interest  for  the  use  of  $250  for  4  yr. 
2  mo.  12  da.,  what  per  cent  do  I  receive  ? 

31.  At  what  per  cent  will  any  given  principal  double 
itself  in  14f  years  ?  In  16|  years  ?  In  8J  years  ? 

33.  The  time  is  5  yr.  3  mo.,  the  rate  is  8$,  and  the  in- 
terest is  $84.  What  is  the  principal  ? 

84.  A  man  loaned  $150  for  a  certain  time,  at  7$,  and 
received  $42  for  the  use  of  the  loan.  For  how  long 
a  time  was  it  at  interest  ? 


CHAPTER  Y: 


MISCELLANEOUS  PROBLEMS. 

-,«.        ^  ** 

fc 


\« 


7.  A  MAN  bought  a  wagon  for  $43,  and  after  paying  $0  for 
having  it  painted,  he  sold  it  at  a  gain  of  $6.     1 : 
did  he  get  for 

j?.  The  parts  are  70,  9,  8,  8,  and  6.     What  is  the  sum  ? 

3.  A  grocer  who  had  100  sacks  of  flour  on  hand  in  the  morn- 
ing, sold  9  sacks  in  the  forenoon,  and  G  in  the  after: 
I  I"\v  many  sacks  had  he  left  at  night  ? 

}.  Kunice  was  7  years  old  9  years  ago.    Marion  is  C 
mire,  and  8  years  older  than  Ruth, 
old  is  Ruth  ? 

5.  A  cotton  broker  sold  to  one  merchant  56  bales  of  eotton, 
to  another  (57  bales,  and  to  another  19  bales  less  than  to 
th.  tins!.  How  many  bales  did  he  sell  in  all  ? 

'  A  drover  bought  37  head  of  eattle  on  Monday,  20  head 
more  on  Tuesday  than  on  Monday,  and  18  head  more  on 

Inesday  than  on  Tuesday.     How  many 
buy? 

7.  Silas  lives  81  rods  nearer  school  than  Ernest.    If  the 
from  home  at  the  same  time,  Silos  walking  9  rods  an<! 
nest    12  rods  a  minute,  they  will   reach   the  school-house 
together.     How  far  does  each  live  from  school  ? 

8.  If  3  men  can  chop  12  cords  of  wood  i.  much 
con  1  man  chop  in  1  day  ? 


MISCELLANEOUS     PROBLEMS.  165 

9.  If  a  man  can  earn  $75  in  3  months,  how  many  months -will 
it  take  him  to  earn  $200  ? 

10.  I  have  two  farms,  that,  together,  contain  134  acres,  and 
one  contains  14  acres  more  than  the  other.    How  many 
acres  would  there  be  in  the  two  farms,  if  each  was  of  the 
size  of  the  smaller  ?     How  many  acres  are  there  in  the 
smaller  farm  ?     How  many  acres  in  the  larger  ? 

11.  A  grocer  has  75  pounds  of  tea  in  two  chests,  one  of  which 
contains  15  pounds  more  than  the   other.     How   many 
pounds  are  there  in  each  chest  ? 

12.  Two  men  earn  $60  in  a  week,  and  one  of  them  cams  $10 
more  than  the  other.     How  many  dollars  does  each  man 
earn? 

13.  Upon  a  vessel  are  105  persons,  and  the  number  of  passen- 
gers is  13  more  than  the  number  in  the  crew.     How  many 
passengers  are  there  aboard  the  vessel  ? 

14.  Ida's  grandmother  is  65  years  older  than  she,  and  the  sum 
of  their  ages  is  87  years.     How  old  is  each  ? 

15.  The  sum  of  two  numbers  is  98,  and  their  difference  is  44. 
What  are  the  numbers  ? 

16.  The  sum  of  two  numbers  is  133,  and  their  difference  is  97. 
What  are  the  numbers  ? 

17.  I  have  49  cents.     If  I  give  to  each  of  5  boys  as  many  cents 
as  I  can,  how  many  cents  will  I  have  left? 

18.  Into  how  many  10- acre  lots  can  a  farm  of  87  acres  be  di- 
vided? 

10.  How  many  plows,  at  $7  apiece,  can  be  bought  for  $60  ? 
%Q.  At  $9  apiece,  how  many  bureaus  can  be  bought  for  $100  3 

21.  A  farmer  having  98  gallons  of  cider,  filled  as  many  10-gal- 
lon  kegs  as  he  could,  and  sold  the  rest  at  26  cents  a  gallon. 
How  many  kegs  of  cider  had  he,  and  how  much  did  he  re- 
ceive for  what  he  sold  ? 

22.  How  many  weeks  and  days  are  100  days  ?     Are  150  days  ? 

23.  What  is  the  width  of  a  room  which  requires  8  breadths  of 
Brussels  carpeting  to  cover  the  floor,  each  breadth  being  2 
ft.  3  in.  wide  ? 


16G  MISCELLANEOUS    PROBLEMS. 

a  horse  eats  6  qt.  of  oats  in  a  day,  how  man 
will  7  bo.  4  qt  last  him? 
25.  A  gardener  sold  5  bo.  3  pk.  of  tomatoes,  at  $.60  a 

Uow  much  did  he  sell  tl. 

J  s«l.  nl.  of  lami  \i«  M  3  bu.  of  potatoes,  how  many 
bushels  will  1  A.  50  sq.  rd.  produce? 

•  w  much  will  2  Ib.  11  oz.  of  1. utter  cost,  at  $.48  per 
pound? 

28.  A  tailor  bought  1 1  gross  8  dozen  of  buttons,  and  used  7 
gross  9  dozen  of  them.    How  many  buttons  had  he  1. 

20.  Nancy  covered  a  box  which  was  10  inches  long,  0  inc-hcs 
:<•,  and  8  inches  deep,  with  gilt   paper.    How  many 
square  inches  of  pajx-r  <li.l  >lu  use? 

50.  The  front  wall  of  a  brick  house  is  25  feet  long,  20  feet  high, 
and  1  foot  th'u-k.     How  many  cubic  feet  does  it  contain, 
allowing  7  cubic  yards  for  the  openings  for  doors 
wind 

.  •'/.  I  low  much  will  1  ream  of  paper  cost,  if  10  sheets  arc 
worth  7  cents? 

51.  If  mackerel  arc  worth  13  cents  a  pound,  how  much  will  a 
barrel  sell  for  ? 

.   If  J  sq.  r.l.  of  land  yield  8  bu.  of  potatoes,  how  many 
bushels  will  1  A.  50  sq.  rd.  produce  ? 

;i  farmer  sows  14  pounds  of  clover  seed  to  the  acre,  how 
many  acres  can  he  sow  with  2  bushels  20  pounds,  allowing 
60  pounds  to  the  bushel  ? 

you  can  count  90  eggs  in  one  minute,  how  many  dozen 
can  you  count  in  an  hour  ? 

36.  A  tinsmith  made  a  8-gallon  rectangular  can,  which  was  7 
by  9  inches  on  the  bottom.     How  many  inches  deep  was 
it.  there  l".inur  '-Ml  cubic  inches  in  a  liquid  gallon? 

37.  If  a  wheel  is  5£  yards  in  circumference,  how  many 
will  it  revolve  in  going  a  mile  ? 

38.  How  much  will  be  the  expense  of  plastering  n  ceiling  27 
feet  long,  and  24  feet  wide,  at  $1  for  every  3  square  yards  ? 


MISCELLANEOUS    PKOBLEHS.  167 

59.  What  is  the  cost  of  2  A.  80  sq_.  rd.  of  land,  at  $50  an  acre  ? 

40.  How  many  cubic  feet  are  there  in  a  stick  of  timber  16 
inches  wide,  9  inches  thick,  and  13  feet  long  ? 

41.  A  publisher  uses  6  sheets  of  book  paper  for  one  copy  of  a 
book  that  contains  288  pages.     How  many  copies  can  he 
make  from  10  reams? 

4S.  How  many  days  are  there  in  the  first  3  months  of  a  com- 
mon year  ?  Of  a  leap-year  ? 

43.  How  many  days  from  Apr.  1  to  Aug.  1  in  any  year  ? 

44.  A  merchant  buys  a  bill  of  goods,  Jan.  1,  on  60  days'  credit. 
When  is  the  payment  due  ? 

45.  On  the  20th  day  of  Sept.  a  man  sold  a  village  lot,  which 
was  to  be  paid  for  in  4  months  15  days.     On  what  day  was 
the  payment  due  ? 

46.  |45  are  £  of  the  cost  of  9  yd.  of  velvet.    At  what  price 
per  yard  must  it  be  sold,  to  gain  20$. 

47.  When  potatoes  sell  at  $1|-  per  barrel  of  2  bu.  3  pk.,  how 
much  is  a  bushel  worth  ? 

48.  A  farmer  having  77  bu.  of  greenings,  kept  \  of  them,  and 
sold  the  remainder  at  $3.12£  per  barrel.     How  much  did 
he  receive  for  them  ? 

49.  f  of  3  times  ££  are  f  of  what  number  ? 

60.  -|  of  6  times  -^  are  -/f  of  what  number  ? 

51.  A  boy  gave  2  cents  more  than  £  of  his  money  for  peaches, 
1  cent  more  than  £  of  the  remainder  for  marbles,  and  had 
4  cents  left.     How  much  money  had  he  at  first  ? 

52.  If  a  boarding-house  keeper  uses  on  an  average  10  Ib.  of 
flour  a  day,  how  many  barrels  will  he  use  in  14  weeks  ? 

53.  If  a  farmer's  family  use  8  Ib.  of  pork  a  week,  how  many 
barrels  will  they  use  in  50  weeks  ? 

64.  A  farmer  drew  4  loads  of  hay,  which  weighed  respec- 
tively 18  cwt.,  1  T.  3  cwt.,  1  T.  2  cwt,  and  17  cwt.  How 
much  hay  did  he  draw  ? 

55.  A  market  gardener  sowed  a  field  of  4£  A.  to  peas,  beets, 
and  onions.  He  had  3|  A.  of  peas,  and  {$  A.  of  beets. 
How  many  acres  of  onions  had  he  ? 


1G8  MISCELLANEOUS     PROBLEMS. 

56.  6f,  5},  and  bow  many  are  16)  ? 
: .  11  100  gal.  flow  from  a  spring  in  9£  h.,  what  part  of  100  gal. 

will  flow  from  the  same  spring  in  5}  h.  f 
68.  In  repairing  a  culvert,  a  pile  of  stone  3$  ft.  Ion- 

and  3  ft.  high  was  used.    What  part  of  a  cord  of  ston 

used? 
59.  At  $f  for  f  of  a  pound  of  English  breakfast  tea,  how 

much  will  }  of  a  pound  cost? 

GO.  The  pier  of  a  bridge  is  24  feet  hiirh,  and  »  of  this  height 
is  twice  the  height  What  part 

of  the  pier  is  above  water? 

01.  At  $7  a  barrel,  how  many  barrels  of  flour  must  be  given 
for  f  of  a  hogshead  of  W.  I.  molasses,  at  $72  a  hogshead  ? 

63.  Two  men  purchased  a  load  of  potatoes,  one  paying  $4,  the 

:  *:j.     What  part  of  the  load  ought  each  to  have  ? 

C5.  Three  men  pay  $20  for  the  use  of  a  piece  of  land,  from 
whi(  h  t!u  v  li:u-\.-t  800  bushels  of  wheat    A  pays  $6,  B 
$0,  and  C  $5.    How  many  bushels  of  wheat  ought  e:. 
have? 

64.  Two  men  joined  in  a  business  transaction,  A  fun 
twice  as  much  money  as  B.  and  they  made  $600. 
much  wa  ich  ? 

65.  B  put  |200  into  n  certain  l>n>inoss,  and  nfler  1  year  A  put 
$400  into  the  business  with  him.     At  the  end  of  two  years 
their  whole  profits  were  $600.     How  much  was  • 

ner's  share  ? 

€6.  Three  men  hire  a  pasture  together,  paying  $40.     A  put  in 
a  horse,  B  4  cows,  and   ('  40  ;  lu-ep.  the  men  agreeing  that 
•  •ws  should  be  considered  cq.ial  to  one  horse,  and  4 
sheep  to  1  cow.     What  ought  each  to  pay  ? 

67.  A  and  B  agreed  to  harvest  a  field  of  wheat  for  $1 1 
sent  4  men  for  5  days,  and  B  5  men  for  G  d;.  :,uch 
ought  each  to  ha\ 

68.  A,  B,  and  C  enter  upon  a  speculation,  A  investing  $* 

B  $70.     They  train  $120,  of  which  TVs  share  is  $48.    What 
should  A  and  i  eivc,  and  what  docs  C  in 


MISCELLANEOUS    PROBLEMS.  169 

69.  A,  B,  and  C  commence  trade  together,  A  investing  twice  as 
much,  and  C  three  times  as  much  as  B.     They  gain  $720. 
How  much  ought  each  to  receive  ? 

70.  A  merchant  tailor's  sales  amount  to  $12,000  a  year ;    his 
average  profits  are  20$  of  his  sales,  and  his  store  expenses 
are  25$  of  his  profits.     How  much  is  his  net  gain  ? 

71.  A  man  sold  a  horse,  which  cost  him  $150,  for  $10  more 
than  $  of  cost.    "What  $  did  he  make  ? 

72.  An  agent,  whose  commission  is  8$,  receives  $5,427  from  his 
principal.     How  much  of  this  sum  will  he  retain  for  his 
commission,  and  how  much  will  he  expend  for  his  prin- 
cipal ? 

73.  16f  $  of  a  certain  farm  is  woodland,  10$  of  it  is  under  til- 
lage, and  the  remainder,  which  is  110  acres,  is  in  meadow 
and  pasturage.    Of  how  many  acres  does  the  farm  consist  ? 

74.  A  grocer  sold  eggs  at  $.20  a  doz.,  which  was  16f  $  less  than 
cost.    For  what  should  he  have  sold  them,  to  make  16£$  ? 

75.  A  sleigh  maker  sold  a  cutter,  which  cost  him  $25,  at  144$ 
advance,  and  another  for  $45,  which  was  25$  less  than  cost. 
How  much  was  his  total  gain  or  loss  in  the  two  transac- 
tions ? 

76.  A  person  found  a  knife,  and  no  one  claiming  it,  he  sold  it 
for  $.25.     What  $  did  he  make  ? 

77.  A  tax  of  $10  is  levied  on  persons  assessed  for  the  following 
amounts  of  property :  $50,  $25,  $75,  $40,  $60,  $25,  $125, 
$150,  and  $250.    What  is  each  one's  share  of  the  tax  ? 

78.  What  is  the  amount  of  $500  for  4  yr.  7  mo.  15  da.,  at  8$  ? 

79.  In  7  yr.,  at  8$,  what  principal  will  amount  to  $117  ? 

80.  For  how  long  a  time  must  $84  be  at  interest,  at  10$,  to 
amount  to  $112? 

81.  A  druggist  buys  perfumery  at  £  off.     What  $  does  he  make 
by  selling  it  at  the  regular  price  ? 

82.  A  gentleman  wishing  to  buy  a  coat,  agrees  to  pay  the  mer- 
chant any  price  he  may  ask  for  the  cloth,  less  100$.     What 

wilHbe  cloth  cost? 


170  MISCELLANEOUS     PROBLEMS. 

83.  Wool  that  crvt  $.-12  per  pound,  shrunk  44  ;  i 

and  after  being  cleansed,  was  sold  at  88|#  above  cost    At 
what  price  per  pound  was  it  sold  ? 

84.  When  the  sum  of  two  parts,  and  one  of  the  parts  are 
given,  how  is  the  other  part  found  ? 

85.  When  the  sum  of  any  number  of  parts,  and  a: 
l»ut  one  are  given,  how  is  that  part  fou: 

86.  When  thr  difference  and  minuend  are  given, 
subtrahend  found  ? 

87.  When  tin-  sulttruhend  and  remainder  are  givm.  IK >v. 
minuend  found  ? 

88.  When  the  greater  of  two  numbers,  or  iflerence  are 
given,  how  is  the  less  number  found  ? 

89.  ^~hen  the  less  of  two  number-  iterance  are 
given,  how  is  the  greater  number  found  i 

90.  To  what,  in  ,  does  the  minuend   in   subtr 
correspond?      To  what  do   subtrahend   and  remui 
correspo: 

01.  How  is  the  product  of  any  numlx-r  of  factors  found  \ 

9S.  When  tho  product  and  one  of  two  factors  arc  given,  how 

is  the  other  factor  found  ? 
03.  When  the  product  of  several  factors,  and  all 

but  one  are  given,  how  is  that  factor  for. 

94.  When  the  product  and  multiplier  are  given,  how  is  the 
multiplicand  found  ? 

95.  When  the  product  and  multiplicand  are  given,  how  is  tho 
multiplier  found  ? 

96.  When  the  dividend  and  quotient  arc  given,  how 
divisor  found? 

.'O.  When  the  divisor  and  quotient  are  given,  ho-.v  is  the  divi- 
dend found  ? 

.°.*.  What  terms  in  multiplication  and  division  correspond  to 
each  other  ? 

99.  What  processes  in  multiplication  and  division  are  converse 
operations  ? 


.A.  1ST  U 

or 

METHODS   AND    SUGGESTIONS. 


TO  TEACHERS.— This  Manual  contains  hints  and  suggestions  intended 
to  aid  you  in  the  successful  use  of  the  book.  Many  suggestions  valuable  in 
mental  work  will  be  found  in  the  Manuals  of  the  other  books  of  this  Series, 
which,  to  avoid  repetition,  have  been  omitted  from  this  work. 

The  Methods  given  in  this  Manual  as  models  of  solution  are  brief,  strictly 
logicalrand  in  accordance  with  the  true  philosophy  of  development;  but  ex- 
perience teaches  that  it  is  not  best  to  require  pupils  to  adhere  rigidly  to  any 
one  method.  Encourage  them  to  solve  problems  in  various  ways :  an  original 
solution,  if  correct,  is  better  them  any  memorized  formula. 

J '<!</<>  9.—  Give  exercises  in  writing  and  reading  numbers  in  the  following 
order : 

1st.  Numbers  expressing  hundreds  only ; 

2rf.  Numbers  expressing  hundreds  and  tens ; 

3d.  Numbers  expressing  hundreds  and  ones ; 

4th.  Numbers  expressing  hundreds,  tens,  and  ones. 

Require  pupils  to  master  thoroughly  each  of  these  classes  of  numbers,  in 
order,  before  passing  to  the  next. 

I'nt/c.  11.—  Pupils  who  have  been  through  the  First  Lessons  in  Numbers, 
in  this  Series,  or  any  similar  work,  may  omit  Sections  II.,  III.,  IV.,  V.,  and 
VI.,  and  commence  at  Review  Problems,  page  52. 

rntff  /.>.  Problem  59.— These  ten  exercises  are  intended  as  a  substitute 
for  the  Addition  Table.  First  require  the  class  in  concert,  and  then  each  pupil, 
to  recite  a  set  of  combinations  repeatedly,  till  all  can  recite  them  correctly  and 
rapidly.  The  combinations  mny  be  mastered  in  three  steps,  as  follows  : 

First  Step.—l  and  1  are  2,  2  and  1  are  3,  3  and  1  are  4,  4  and  1  are  5,  and  so 
on,  to  10  and  1  are  11 ;  then  reversing  the  order,  10  and  1  are  11,  9  and  1  arc  10, 
8  and  1  are  9,  and  so  on,  to  1  and  1  arc  2. 

Second  Step.—l  and  1  are  2, 1  and  2  arc  3, 1  and  3  are  4, 1  and  10  are 

11, 1  and  9  are  10, 1  and  8  are  9 

Third  Step.—l  and  1  are  2,  2  and  1  or  1  and  2  are  3,  3  and  1  or  1  and  3  are  4, 

4  and  1  or  1  and  4  are  5 10  and  1  or  1  and  10  are  11,  9  and  1  or  1  and  9  are 

10,  8  and  1  or  1  and  8  are  9 

/'"r/''  17.  Problem  93.— The  suggestions  under  the  last  reference  may  be 
applied  to  drills  upon  this  and  the  next  four  pages. 

J>ftr/t:  21.  Problem  192.— Pupils  will  acquire  familiarity  with  the  com- 
bination of  any  two  figure*,  by  being  questioned  in  the  following  manner:— 
When  1  is  added  to  any  number  whose  right-hand  figure  is  0,  what  is  the 
right-hand  figure  of  the  sum  ?  What  is  it,  when  the  right-hand  figure  is  1  ? 


ITS  MANUAL. 

• 

What,  when  I  tU  2?  When  it  in  3  r  4?  etc.  What  i*  the  right-hand-figure  of 
the  ram,  when  9  is  added  to  any  nmnbor  whose  right-hand  figure  Is  0?  1?  8? 
8?  etc.  Ask  similar  questions  for  3,  4,  5. 

-•7.  Problem  65.—  These  ten  exercises  arc  intended  a*  a  eu 
for  the  Subtraction  Table.  A  method  of  drill  should  be  adopted  f. 
combination*,  similar  to  the  method  for  those  in  addition  given  on  j.:. 

IVoblem  lOO.-Snggcstlons  nnder  the  last  reference  may  bo 
applied  to  drills  upon  the  combinations  given  in  the  exercises  on  t 
five  pages. 

/•-••<    /  /.    Problem  61.—  Tho  next  nine  problems  are  Intended  as  a  sub- 
stitute for  the  Multiplication  Table.    These  drills  should  be  graded  in  three 


Ftrtt  5fcp.-0nce  S  1s  t,  9  times  S  are  four,  8  times  2  are  6,  4  times  I  are 
10  times  2  are  X):  then  reversing  the  order,  10  times  9  are  SO,  0  times 
2  are  18,  8  times  2  are  10,  .....  once  I  Is  S. 

Bteond  Stop.—  3  times  1  are  2,  2  times  9  are  4,  2  times  8  are  «,  9  times  4  are  8, 
and  so  on:  2  times  10  are  20,  «  times  9  are  18,  2  times  8  are  16,  and  so  on. 

Third  Sffp.-Oncc  2  or  2  times  1  are  2,  2  times  2  are  4,  8  times  2  or  2  times  8 
are  6,  4  times  2  or  2  times  4  are  8,  and  so  on  :  10  times  2  or  2  times  10  are  90,  9 
times  2  or  2  times  9  are  18,  8  times  2  or  2  times  8  arc  1C,  and  so  on. 

49.    Problem  S.-Lead  the  pupil  to  deduce  the  process  of  division 
from  subtract  i  in  this  problem,  1  load  of  a  hogsheads  taken  from  13 

hogsheads  tares  9  hogsheads,  1  load  more  taken  leaves  6  hogsheads,  and  so 
on.  Then  he  has  taken  1  load,  and  1  toad,  and  1  load,  and  1  load,  or  4  loads. 

raffr  St.  Problem  124.  -The  remaining  exercises  In  this  Section,  com- 
mendng  with  119,  are*  a  substitute  fur  both  forms  of  the  Division  Table. 
These  drills  may  be  graded  in  three  stepe,  as  follows  : 

Ftrtt  Step.—  Require  the  pupil  to  go  through  with  each  exercise  separately, 
until  he  makes  no  mistakes  ;  thus,  Exercise  H9,-2  in  2  once,  9  in  4  2  times,  t 
in  6  8  times,  2  in  8  4  times,  and  so  on  ;  then,  reversing  the  order,  2  in  20  10 

<•-,  2  in  10  8  times,  and  so  on. 

>e  122.-*  of  2  Is  1,  v  of  4  is  2,  ,  of  6  Is  8,  i  of  8  is  4,  and  so  on  ;  and  i  of 
20  is  10,  ft  of  18  is  9,  t  of  16  Is  8,  and  so  on. 

Second  Sttp.—  Rcqnirc  the  pupil  to  change  divisor  and  quotient  with  each 

vi-,-  no.  -2  In  2  once,  2  in  4  2  times,  2  In  0  8  times  and  8 

In  6  2  times,  S  In  8  4  times  and  4  in  8  2  times,  and  so  on  ;  2  in  20  10  times  and 

10  in  20  2  times,  2  in  18  9  times  and  9  in  18  2  times,  2  in  16  8  times  and  8  in 

16  2  times,  and  so  on. 

Exercise  122,—  i  of  2  Is  1,  *  of  4  is  2,  ft  of  6  is  8  and  }  of  6  Is  1  ft  of  8  is 
4  and  J  of  8  is  2,  *  of  10  is  5  and  J  of  10  is  2.  and  so  on  ;  |  of  80  is  10  and  ,',  of 
20  is  2,  i  of  18  is  9  and  I  of  18  is  2,  ft  of  16  is  8,  and  }  of  16  is  2,  and  so  on. 

Third  Step.—  Combine  the  exercises  that  contain  the  same  results,  as  Exer- 
cises 119  and  122.  120  and  123,  and  so  on.-and  recite  them  as  fellows-taking 
Exercises  120  and  123  for  exampl  :  ce.  \  of  3  is  1  ;  3  in  6  2  times  and 

2  in  6  3  times,  i  of  6  is  2  and  i  of  6  is  3;  3  in  9  3  times,  J  of  9  i  - 
times  and  1  in  '  of  IS  is  4  and  i  of  12  is  8  ;  3  in  15  5  times  and  5  in 

i:>  3  times  '  of  15  i»  5  and  J  of  15  is  8;  and  so  on  ;  then  in  reverse  order.  8  in 
30  10  times  and  10  in  80  3  times,  \  of  30  is  10  and  A  of  30  is  3;  3  in  27  9  times 
and  9  in  27  3  times,  i  of  27  is  9  and  J  of  27  is  8:  and  so  on. 


MANUAL.  173 

Par/f-  S3.  Problems  15, 16. — It  is  good  practice  fo  require  pupils  to  draw 
diagrams  for  use,'iu  solving  problems  like  these  two;  also,  to  require  them  to 
solve  problems  in  as  many  different  ways  as  possible. 

Pnf/f  .7.7.  Problem  44.— Require  pupils  to  recite  the  factors  of  all  the 
composite  numbers  in  order,  to  100  inclusive.  See  Factor  Table,  First 
Lessons  in  Numbers,  page  107. 

I'itf/c  ,7<';.  Problem  CO.— The  drill  upon  each  of  these  5  sets  of  exercises 
should  be  in  two  steps. 

/\'/vtf  Step.— Lei  the  pupilo  recite  each  exercise,  thus— 5  is  £  of  2  times  5  or 
10,  5  is  i  of  3  times  5  or  13,  5  is  J  of  4  times  5  or  20,  and  so  on ;  then  reversing 
the  order,  5  in  ^  of  10  times  5  or  50,  5  is  J  of  9  times  5  or  45,  5  is  J  of  8  times 
5  or  40,  and  so  on. 

Second  Step.— 5  is  J  of  10,  5  Is  %  of  15,  5  is  J  of  20,  and  so  on ;  and  then,  5  is 
^  of  50,  5  is  J  of  45,  5  id  £  of  40,  and  so  on. 

Pago  56.  Problem  80.— Pupils  should  complete  this  book  to  this  place, 
before  commencing  the  study  of  the  Common  School  Arithmetic.  From  this 
place  the  same  subjects  in  the  two  books  should  bo  studied  in  connection. 

Pttfjr  f>.">.  Problem  18. — Give  pupils  considerable  practice  in  separating 
given  dividends  into  parts  which  are  exact  multiples  of  the  given  divisors. 
Thus  81  -*-  7,  84  =  70  +  14 ;  56  +  4,  5C  =  40  +  10 ;  90  -*-  G,  96  =  CO  +  30. 

Pntjo  84.  Liquid  Measure.— Every  school-house  should  be  supplied  with 
the  following  weights  and  measures,  to  be  used  by  the  pupils  while  learning 
the  tables  of  Compound  Numbers :  a  liquid  pint,  a  quart,  and  a  gallon  measure 
of  tin ;  a  dry  quart,  i  peck,  peck,  and  i  bushel  measure  of  wood,  and  a  bushel 
br.sket ;  a  foot-rule  divided  into  inches,  a  yard-stick,  and  a  tape  measure  or 
string  at  least  1  rod  long;  a  cubic  inch,  and  a  cubic-foot,  of  wood  or  paste- 
board ;  a  balance  or  a  pair  of  pastry  scales  with  1  oz.,  2  oz.,  4  oz.,  8  oz.,  1  lb., 
2  lb.,  and  4  lb.  weights  (or  if  the  scales  and  weights  can  not  be  had,  sacks  of 
eand  or  shot  of  these  several  weights  distinctly  marked). 

J'ftr/c  94.  Time.— Children  have  an  imperfect  appreciation  of  the  three 
smallest  denominations  of  time.  It  will  be  found  a  good  exercise  to  require 
them,  first  in  concert,  then  singly,  to  beat  and  audibly  count  seconds,  first  10 
seconds,  then  20,  then  30  or  i  minute.  After  thin,  require  them  to  count 
silently  I  minute,  then  a  minute,  and  to  raise  hands  when  they  are  through, 
the  exact  time  being  noted  by  the  time-piece.  Again,  all  the  school  may  be 
required  to  eit  still  1  minute,  then  2,  3,  4,  and  5  minutes  successively. 

Page  96.  Problems  100, 107.— Give  several  problems  like  these  two,  show- 
ing that  the  length  of  the  day,  i.  <?.,  from  sunrise  to  sunset,  is  equal  to  double 
the  time  of  the  sun's  setting;  and  the  length  of  the  night,  f.c.,  from  sunset 
to  sunrise,  is  equal  to  double  the  time  of  the  sun's  rising. 

Page  139 — Problems  16, 17, 18  illustrate  the  manner  in  which  the  conditions 
of  a  problem  may  be  eo  varied  as  to  form  several  problems.  Each  of  the  prob- 
lems In  Sections  I.  and  II.  should  be  varied  in  a  similar  manner  by  the  class. 

J'df/c.  14 1.  Problem  1. — These  problems  in  Reductions  maybe  made  to  af- 
ford double  practice,  by  requiring  pupils  to  form  and  solve  the  converse  of  each. 

Page  144.  Problem  3. — In  Percentage,  require  pupils  to  give  the  per  cent, 
first  in  hundredths,  and  then  in  a  common  fraction  reduced  to  its  lowest  terms. 

Pfigc  158.  Problem  3-1.— Require  pupila  to  form  and  eolvc  the  converse 
of  each  of  these  problems. 


/'</'/''  11.    1-  (1.)  There  are  5  boys  in  the  group  ;  because  8 
boys  and  2  boys  are  5  boys.    Or, 

There  are  in  the  group  8  boys  and  2  boys,  which  are  5  boys. 
2.  1  tree  and  2  trees  are  3  trees. 

Page  12.    82.  (1.)  He  shot  12  birds;  because  pigeons  and 
quails  are  birds,  and  10  birds  and  2  birds,  are  12  birds.    or. 
(2.)  Since  pigeons  and  quails  are  birds,  he  shot  10  birds  and  2 

which  are  12  birds. 

!'"</<*  22.    1.  We  can  see  two  largo  windows;   because  1 
window  from  3  windows  leaves  2  windows. 

5.    (1.)  2  are  girls  ;  because  2  children,  the  boys,  from 
rhil.lrm  h-iivo  2  children,  the  girls. 
(2.)  4  children  leas  2  children,  the  boys,  are  2  child  r 


Page  23.  1L  (1.)  He  has  5  doves  ;  because  2  doves  from  7 
doves  leave  5  doves.  Or, 

(2.)  He  has  7  doves  less  2  doves,  which  are  5  doves. 

I'iff/e  26.  46.  7  and  4  more  arc  11  ;  because  7  from  11  leaves  4 

Pd(/<  :>  !>.  r.  54-9  is  the  greater  ;  because  54-9=45,  and 
49-6=43,  and  45  is  greater  than  43. 

Page  35.  1.  (1.)  He  expended  16  cents;  because  5  cents,  4 
cents,  and  7  cents  are  16  cents.  Or, 

lie  expended  5  cents,  4  cents,  and  7  cents,  which  are  16 
cents.  Or, 

(8.)  He  expended  the  sum  of  5  cents,  4  cents,  and  7  cents, 
which  is  16  rents. 

1  .)  He  has  given  away  5  peaches  and  4  peaches,  which  are 
9  peaches  ;  and  he  has  left  9  peaches  less  9  peaches,  which  are  0 
peaches.  Or, 

(2.)  From  the  9  peaches,  he  gave  5  to  Adah,  which  loft  him  4 
peaches,  Then  from  the  4  peaches,  he  gave  4  to  Juliet,  which 
leaves  him  0  peache*. 


METHODS.  175 

Page  35.  12.  When  the  tide  rises  7  feet,  the  rock  will  be  7 
feet  and  7  feet;  or  14  feet,  under  water ;  and  afterward,  when  it 
falls  9  feet,  the  rock  will  be  14  feet  less  9  feet,  or  5  feet,  under  water. 

Page  38.  16.  (1.)  They  will  cost  $16  ;  because  2  times  $8 
are  $16.  Or, 

(2.)  They  will  cost  2  times  $8,  which  are  $16. 

Page  42.  5.  (1.)  You  can  buy.  4  peaches ;  because  2  cents 
are  contained  in  8  cents  4  times.  Or, 

(2.)  Since  the  number  of  times  2  cents  are  contained  in  8  cents 
equals  the  number  of  peaches,  and  2  cents  are  contained  in  8 
cents  4  times,  you  can  buy  4  peaches. 

Page  43.  22.  (1.)  There  will  be  4  cows  ;  because  \  of  8 
cows  is  4  cows.  Or, 

(2.)  In  each  pasture  there  will  be  \  of  8  cows,  which  is  4  cows. 

Page  52.  2.  In  4  weeks  the  father  earns  4  times  $9,  or 
$36  ;  in  1  week  the  son  earns  $4 ;  and  both  earn  in  all  $36  and 
$4,  which  are  $40. 

Page  53.  9.  He  sold  the  4  melons  for  4  times  9  cents,  or  36 
cents  ;  and  the  slate  cost  him  36  cents  less  6  cents,  which  are  30 
cents. 

Page  54.  32.  It  will  take  9  times  as  many  men  to  dig  the 
ditch  in  1  day  as  to  dig  it  in  9  days,  and  9  times  3  men  are  27 
men. 

41.  4  times  9  are  36,  and  36  is  6  times  6. 

Page  55.    55.  2  times  10  are  20,  and  £  of  20  is  4. 

Page  50.  71.  The  three  barrels  cost  the  sum  of  $7,  $9,  and 
$11,  which  is  $27  ;  and  the  average  price  is  ^  of  $27,  which  is  $9. 

Page  57.  1.  The  cost  of  both  is  the  sum  of  $10  and  $30, 
which'  is  $40. 

Page  58.  S.  I  paid  for  both  the  sum  of  30  cents  and  14 
cents.  14  cents  are  10  cents  +  4  cents.  30  cents  and  10  cents 
are  40  cents,  and  40  cents  and  4  cents  are  44  cents.  Hence,  I  paid 
44  cents  for  both. 

17.  Both  cost  him  the  sum  of  21  cents  and  18  cents.  21  cents 
and  10  cents  are  31  cents,  and  31  cents  and  8  cents  are  SO  cents. 
Hence,  both  cost  him  39  cents. 

rage  59.  L  He  paid  the  difference  between  $30  and  $10, 
which  ia  $20. 


I',')  METHOD      . 


(51.     77.  There   was  left  the  difference  1 
yards  and  15  yards.     10  yards  from  39  yards  leave  29  yards,  and 
5  yards  from  29  yards  leave  24  yards.     Hence,  24  yards  wi 
in  the  j 

I  '<!!/<    <'>  9.       .  4  shawls  will  cost  4  times  as  much  as  1  I 
and  4  times  $30  are  $120. 

:  pounds  will  cost  3  times  as  much  as  1  pound  3  times  20 
cents  are  60  cents,  8  times  8  cents  are  9  cents,  and  GO  cents  +  9 
cents  are  09  cents.  Hence,  8  pounds  will  cost  69  cents. 

yv/f/r  *;:;.  r.ir  4  bales  of  imjr*  1  \\\\\^  •.  ist  be 

paid  as  for  1  bale.    4  times  $40  are  $160,  4  times  $4  arc  *1G,  and 
$160  +  $16  are  $176.    Hence,  $176  must  be  paid  for  4  bales. 
/'</'/'    />'  /.          l  ;  -ml  will  cost  i  as  much  as  4  yards,  m 
80  cents  is  20  cents. 

yv/r/r  f>'.7.     //.  The  daily  average  was  ^  of  the  nun 
,  thrrsh.nl  in  :J  days,  that  is,  i  of  48  bushels.    48  1. 
are  30  bushels  +  18  bushels.     }  of  30  bushels  is  10  bushels,  \  of 
18  bushels  is  6  bushels,  and  10  bushels  +  6  bushels  an 

.  tli,-  daily  :iv.-rage  was  16  bushels. 

15.  The  number  of  times  9  loaves  are  contained  in  108  loaves 
equals  the  number  of  weeks.  9  loaves  are  contained  in  90  loaves 

•  -3,  in  18  loaves  2  times,  and  10  times  and  2  t 
times.    Hence,  108  loaves  will  last  them  12  weeks. 

/X'/'  rr. 

10  mills  arc  contained  in  S?  mills  equals  the  11111;  ;its,  and 

tin-  remainder  equals  the  number  of  mills.    87  mills  are  80  mills 

M-atest  part  that  will  contain  10  mills)  and  7  mills 
maimler).     10  mills  are  contained  in  80  mills  8  times. 
mills  are  8  cents  7  mills. 

yv/r/r  ;.<>.  li  pave  the.  sum  of  $1.50,  $.88,  and  $1.25. 
$1.50  and  $.88  are  $2.88  ;  $2.88  and  $1  are  $8.88,  and  $3.88  and 
$.25  are  $3.63.  Hence,  he  gave  $3.63  for  all. 

ile  had  left  the  difl  $5.84  and  $1.56.     $1 

from  $5.84  leaves  $184,  and  $.50  from  $4.84  leave  $4.28.     ' 
he  had  $4.2S  Irft. 

I'ttf/e  SO.     1~>.  In  6  days  he  will  earn  6  times  as  :.. 
1    day!     0  timrs 
$4.50;  and  $6  +  $i.50  arc  $10.50.     Hence,  he  will  earn  $10.50. 


METHODS.  177 

Page  80,  20.  1  yard  will  cost  £  as  much  as  5  yards.  $1.85 
are  $1.50  + $.35.  i  of  $1.50  is  $.30,  £  of  $.35  is  $.07,  and  $.30  + 
$.07  are  $.37.  Hence,  1  yard  will  cost  $.37. 

The  number  of  times  $.08  are  contained  in  $2.24  equals  the 
number  of  pounds.  $2.24  are  $1.60 +  $.64.  $.08  are  contained 
in  $1.60,  20  times,  in  $.64,  8  times,  and  20  times +  8  times  are  28 
times.  Hence,  23  pounds  can  be  bought. 

Page  84.  2.  7  qt.  are  7  times  as  many  pints  as  1  qt.,  and  7 
times  2  pt.  are  14  pt.  14  pt.  are  14  times  as  many  gills  as  Ipt., 
and  14  times  4  gi.  are  56  gi.  Hence,  7  qt.  are  56  gi. 

4.  In  as  many  days  as  there  are  gills  in  4  gal.  1  qt.  1  pt.  3  gi. 
4  gal.  are  4  times  4  qt,,  or  16  qt.,  and  16  qt.  + 1  qt.  are  17  qt.  17 
qt.  are  17  times  2  pt.,  or  34 pt.,  and  34  pt.  + 1  pt.  are  35  pt.  35  pt. 
are  35  times  4  gi.,  or  140  gi.,  and  140  gi.  +  3  gi.  are  143  gi.  Hence, 
she  would  use  4  gal.  1  qt.  1  pt.  3  gi.  in  143  days. 

Page  85.  0.  He  used  as  many  gallons  as  are  equal  to  180 
gills.  Since  every  4  gi.  are  1  pt.,  and  4  gi.  are  contained  in  180 
gi.  45  times,  180  gi.  are  45  pt.  Since  every  2  pt.  are  1  qt.,  and  2 
pt.  are  contained  in  45  pt.  22  times,  with  a  remainder  of  1  pt.,  45 
pt.  arc  22  qt.  1  pt.  Since  every  4  qt.  are  1  gal.,  and  4  qt.  are  con- 
tained in  22  qt.  5  times,  with  a  remainder  of  2  qt.,  22  qt.  are  5 
gal.  2  qt.,  and  22  qt.  1  pt.  are  5  gal.  2  qt.  1  pt  Hence,  he  used  5 
gal.  2  qt.  1  pt. 

l*(tge  88.  30.  A  surface  4  ft.  wide  contains  4  times  as  many 
square  feet  as  a  surface  of  the  same  length  1  ft.  wide.  A  surface 
10  ft.  long  and  1  ft.  wide  contains  10  sq.  ft.,  and  4  times  10  sq.  ft. 
are  40  sq.  ft.  Hence,  the  black-board  has  40  sq.  ft.  of  surface. 

^?.  Since  every  inch  in  width  of  the  surface  measures  10  sq.  in., 
the  number  of  tunes  10  sq.  in.  are  contained  in  80  sq.  in.  equals 
the  number  of  inches  in  the  width  of  the  slate.  10  sq.  in.  are 
contained  in  80  sq.  in.  8  times.  Hence,  the  slate  is  8  in.  wide. 

I*age,  f)O.  5G.  A  block  6  in.  wide  contains  6  times  as  many 
cubic  inches  as  a  block  1  in.  wide  ;  a  block  3  in.  thick  contains  3 
times  as  many  cubic  inches  as  a  block  1  in.  thick  ;  and  a  block 
12  in.  long,  1  in.  wide,  and  1  in.  thick,  contains  12  cu.  in.  6  times 
12  cu.  in.  are  72  cu.  in.,  and  3  times  72  cu.  in.  are  216  cu.  in. 
Hence,  the  block  contains  216  cu.  in. 

<'><>.  Since  every  foot  in  length,  of  a  body  2  ft.  wide  and  3  ft. 
thick,  contains  6  cu.  ft.,  the  number  of  times  6  cu.  ft.  are  contained 

14 


178  METHODS. 

in  72  cu.  ft.  equals  the  number  of  feet  in  the  length  of  the  box. 
0  cu.  ft.  are  contained  in  72  cu.  ft   12  times.     I:  box  is 

long. 

!'<(</<    </,S.     .;.  1 1«- sold  the  sum  of  5  gal.  2  qt,  3gal.  1  qt  ..ami 
4  gal.  2  qt.    5  gal.  2  qt.  +  3  gal.  are  8  gal.  2  qt.,  8  gal.  2  qt.  +  1  qt. 
arc  8  gal  3  qt.,  8  gal.  3  qt.  +  4  gaL  are  12  gal.  3  qt.,  and 
8  qt.  +  2  qt.  are  12  gal.  5  qt.,  or  13  gaL  1  qt.  Hence,  he  sold  18  gal.  1  qt. 

/'</</'    .'/.'>.    2.  He  had  left  the  difference  between  12  Ib.  6  oz. 
and  5  Ib.  8  ox.     12  Ib.  6  oz.  less  5  Ib.  are  7  Ib.  6  oz.,  an 
6  oz.  less  8  oz.  are  0  Ib.  14  oz.    Hence,  he  hadO  ll>.  1 

l'<rt/c  1OO.     1.  To  fill  5  canisters,  it  will  take  5  times  as 
much  a.*  to  fill  1  canister,  or  5  times  2  Ib.  8  oz.    5  times  2  Ib.  arc 
10  Ib.,  5  times  8  oz.  are  40  oz.,  or  i!  Ib.  8  oz..  and  10  Ib.  +  2  Ib.  8  oz. 
Ib.  8 oz.    Hence,  it  will  take  12 Ib.  8 oz.  to  fill  5  canisters. 

l'»f/r  1O1.  2.  To  seed  1  acre, it  will  take  i  as  many  oats  as 
to  seed  5  acres,  or  fc  of  13  bu.  3  pk.  i  of  10  bu.  h  2  l.u.,  3  bu. 
8  pk.  are  15  pk.,  }  of  15  pk.  are  8  pk.,  and  2  bu.  +  3  pk.  are  2  bu. 
3  pk.  Hence,  it  will  take  2  bu.  8  pk.  to  seed  1  acre, 

/  '<{>/<    /  1O.    9.  1  cu.  yd.  is  H  cu.  yd.,  i  cu.  yd.  Is  /r  c 
and  the  number  of  times  /?  cu.  yd.  are  contained  in  i?  cu  yd. 
equals  the  number  of  thirds.     -,y:  cu.  yd.  arc  contained  in  $  f  cu.  yd. 
2  times.    Hence  H  cu.  yd.  are  §  cu.  yd. 

I '<i'!>  111.  14,  Since  the  value  of  a  fraction  is  not  changed 
by  dividing  both  of  its  terms  by  the  same  number,  we  divide 
both  by  the  common  factor  4.  and  obtain  ?  ;  and  since  2  and  7  are 
prime  to  each  other,  the  fraction  f  is  in  its  lowest  terms. 

32.    1  Ib.  is  \\  Ib.,  i  Ib.  is  i  as  many  sixteenths  as  1  Ib.,  and 
$  Ib.  are  5  times  as  many  sixteenths  as  i  Ib.    i  of  1  §  Ib.  is 
and  5  times  ft  Ib.  are  }§  Ib.    Hence,  $  Ib.  are  jg  Ib. 

I'<Kt<    ll.i.     ~>9.  (1)  Since  each  denominator  must  be  a  fac- 
tor  of  the  common  denominator,  sevenths  and  ninths  can  be  re- 
duced to  sixty-thirds.     Multiplying  both  terms  of  $  by  9 
|$,  and  both  terms  of  $  by  7  gives  ,  v     Hence,  5  and  £  equal  the 
similar  fractions,  * J,  an 

Since  (}'•}  \*  the  product  of  7  and  9,  sevenths  and  ninths  can 
be  reduced  to  sixty-thirds.     Multiplying  both  terms  of  $  bv 

r<tt/<  1 14.  V.'t.  i  ft.  are  1  ft.,  and  the  numlx-r  of  times  J  ft. 
are  contained  in  5  ft.  equals  the  number  of  "  \  ft.  are 

contained  in  f  ft.  2  times,  with  a  remainder  of  \  ft.     Hence,  J  ft 
eqnnls  ^  ft. 


METHODS.  179 

Page  115.  09.  8  is  8  times  as  many  ninths  as  1.  1  is  jf,  8 
times  |  are  ^,  and  V  + 1  are  z^.  Hence,  8  J  are  V- 

Page  116.  15.  In  the  two  days  he  cut  the  sum  of  £  and  £  of 
it.  f=ff.f=H>  and  H +*$=*!•  Hence,  he  cut  fj  of  the  meadow 
ia  the  two  days. 

Page  118.  8.  Ho  had  left  the  difference  between  $£  and 
$i.  !*=$&  $I=$A-,  and  $*{}-$&=$&.  Hence,  he  had  $& 
left. 

Paflre  119.  10.  (1.)  She  is  now  13  yr.  less  f  yr.  old.  13  yr. 
=12yr.  +  £yr,  £  yr.-g-  yr.=f  yr,  and  12  yr.  +  f  yr.=12£  yr. 
Hence,  she  is  now  12 J  yr.  old.  Or, 

(2.)  She  is  now  13  yr.  less  f  yr.  old.  13  yr.=fi^yr.f  and  fi05  yr. 
—  |  yr.=V-  yr.,  or  12J  yr.  Hence,  etc. 

££  He  had  left  the  difference  between  1H  bu.  and  -fa  bu.  11J- 
bu.=10  bu.  +  H  bu.  or  £  bu.  or  \$  bu.  |f  bu.— -fa  bu.=W  bu.,  or 
§  bu.,  ard  10  bu.  +  $  bu.=10}  bu.  Hence,  he  had  10}  bu.  left. 

Page  12O.  3.  6  bu.  will  cost  G  times  as  much  as  1  bu,  or 
G  times  $*.  6  times  $J  are  $162-,  or  $2f.  Hence,  G  bu.  will  cost 
$2*. 

Page  121.  24-  15  bar.  will  cost  15  times  as  much  as  1  bar., 
or  15  times  $7-,V  15  times  $7  are  $105  ;  15  times  $  -fa  are  $*/\f ,  or 
$10i;  and  $105 +  $10^  are  $115$.  Hence,  15  bar.  will  cost  $115^. 

29.  \  cd.  will  cost  {  as  much  as  1  cd,  or  ^  of  $5.  i  of  $5  is  5 
times  as  much  as  £  of  $1.  i  of  $1  is  $K  and  5  times  $Jr  are  $|. 
Hence,  i  cd.  wiU  cost  $|. 

P«(7C  J^^.  57.  f  lb.  will  cost  3  times  i  of  the  cost  of  1  lb., 
or  3  times  $•  of  60  cents,  i  of  60  cents  is  7i  cents,  and  3  times 
7J  cents  are  22$  cents.  Hence,  f  lb.  will  cost  22^  cents. 

Page  123.  GS.  In  2J  h.  a  train  will  run  2J  times  as  far  as 
in  1  h,  or  2J  times  24  mi.  2  times  24  mi.  are  48  mi,  J  times  24 
mi.  are  18  mi.,  and  48  mi. +  18  mi.  are  66  mi.  Hence,  the  train 
will  run  66  mi. 

80.  £  gal.  will  cost  3  times  as  much  as  i  gal.  or  3  times  ± 
of  $£.  i  of  $}  is  $i,  and  3  times  $£•  are  $2-.  Hence,  f  gal.  will 
cost  $J. 

Paf/e  .1^4.  57.  f  of  {  yd.  are  3  times  as  much  as  i  of  I  yd. 
*  yd.=2&  yd,  i  of  ^  yd.  is  -fa  yd,  and  3  times  fa  yd.  aro  Ji  yd. 
Hence,  ^  of  $  yd.  are  Jfc  yd. 


180  M  KT  II  0  DS. 


)  The  number  of  times  $|  are  oonta: 
-$  V,  and  $|  are  con 
in  $  .-a    Hence,  10}  bushels  can  be  bought      < 

timber  of  times  $}  are  contained  in  $4  equals  the 
i  usliela    $}  are  contained  in  $4  i  as  many 
as  $1.    $i  is  contained  in  $1  8  times,  in  $i  4  times  h 

s  are  V  times,  Of 

I'tit/r   !.;<>.  (I.)  The  number  of  times  $1  is  cor 

in  $,**  equals  the  numlx-r  of  gallons.     $i=$  A,  and  4  twelfths  of 

contained  in  7  twelfths  of  a  dolL  • 
Hence,  1J  gallons  can  bo  bought.    Or, 

number  of  times  $i  ia  contained  inffr  equ: 
number  of  gallons.     $1  is  contained  in  .7  1  ::  times,  in  $,4  i1*  of  3 

'.  times. 
and  7  tim«  s  ;  time  ur.-  1  ;  times.    Hence,  • 

/>/'/<     /  •"•  '•'.  The  number  of  times  1§  Ib.  are  con 

11>.  equals  the  number  of  days,    llflb.r     ,   11>  .  1 
and  .*>  thirds  of  a  pound  are  contained  in  :r»  tliinls 
/-     /•//.     ,'    5  jral.  =  5  of  4qt.  are  Vqt-,  <>r  -Jj  qt.  :  i  qt.= 
r  1  pt.;  n:  1  j.t.     Hence,  f  gal.= 

)  qt.  1  i>t. 

r<r<,<     1  /.;.  1         is  ipk.,  5  qt.  are  5  pk.,  and  1  pk.+ 

i  pk.=lj  pk.,  or  V  pk.     1  i  i  ,  and  V  P^.  are  J, 

i  bu  ..  or  \l  bu.     Hence,  1  pk.  5  qt.  =  ^|  bu. 
rtn/f   It',.    .?.  Since  2W  are  flfo  ^e  «>ld  -ftft  or  i  of  500 

.  bushehi. 

/V/r/r   //^'.   /4-  150  sheep  arc  iJo.  or  i  of  450  sheep.  Since  430 
sheep  are  100  £,  150  sheep  are  i  of  100*,  or  83i*. 

rnf/r   in.  "ce  he  gained  $500  by  selling  I 

above  cost,  $500  ia  252  or  }  of  the  cost,  and  the  whole  cost  is  4 
times  $500,  or  $2,000.    Or, 

net,  100£,  the  whole  cost,  is  100 
I  A  of  $->00,  which  is  $2.000. 

33.  Since  th<>  inapl««  wood  is  worth  'JO-  more  than  the  oak,  it  is 
worth  $7.50  +  20?,  or  i  of  $7.50.    i  of  $7.50  is  $1  .50,  and  s 
si  "''i  are  $9.     Henc--,  th.>  maple  wood  is  worth  $9  a  cord. 

1  00*  +  50*.  or  150    of  the  number 
.iids  he  bought   at  tin-   first  iVtory  ;  and 
9,000  Ib.  are  ?  of  2  times  ;  of  9,000  Ib.,  which  arc  6,000  Ib.     ! 
ho  bought  6,000  Ib.  at  the  first  factory. 


TA 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


Franklin  Si: 


i.  FRENCH'S  ARITHMET: 


II.  HARPER'S  WRITING  BOOKS. 


III.  HARPER'S  SCHOOL  AND  FAMILY  SLATE, 

lozen. 


